Skip to main content

Some Results from Classical Statistics

  • Chapter
  • First Online:
  • 140k Accesses

Part of the book series: Springer Series in Statistics ((SSS))

Abstract

In this section we provide some definitions and state some theorems (without proof) from classical statistics. More details can be found in Schervish (1995). Let \(\textbf{y} = {[{y}_{1},\ldots,{y}_{n}]}^ T\) be a random sample from p(y∣θ).

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Agresti, A. (1990). Categorical data analysis. New York: Wiley.

    MATH  Google Scholar 

  • Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B.N. Petrov & F. Csaki (Eds.), Second International Symposium on Information Theory (pp. 267–281). Budapest: Akademia Kiado.

    Google Scholar 

  • Allen, J., Zwerdling, R., Ehrenkranz, R., Gaultier, C., Geggel, R., Greenough, A., Kleinman, R., Klijanowicz, A., Martinez, F., Ozdemir, A., Panitch, H., Nickerson, B., Stein, M., Tomezsko, J., van der Anker, J., & American Thoracic Society. (2003). Statement of the care of the child with chronic lung disease of infancy and childhood. American Journal of Respiratory and Critical Care Medicine168, 356–396.

    Article  Google Scholar 

  • Altham, D. (1991). Practical statistics for medical research. Boca Raton: Chapman and Hall/CRC.

    Google Scholar 

  • Altham, P. (1969). Exact Bayesian analysis of a 2 ×2 contingency table and Fisher’s ‘exact’ significance test. Journal of the Royal Statistical Society, Series B31, 261–269.

    MathSciNet  Google Scholar 

  • Arcones, M., & E. Giné. (1992). On the bootstrap of M-estimators and other statistical functionals. In R. LePage & L. Billard (Eds.), Exploring the limits of bootstrap. New York: Wiley.

    Google Scholar 

  • Armitage, P., & Berry, G. (1994). Statistical methods in medical research, third edition. Oxford: Blackwell Science.

    Google Scholar 

  • Bachrach, L., Hastie, T., Wang, M.-C., Narasimhan, B., & Marcus, R. (1999). Bone mineral acquisition in healthy Asian, Hispanic, Black and Caucasian youth. A longitudinal study. Journal of Clinical Endocrinology and Metabolism84, 4702–4712.

    Google Scholar 

  • Bahadur, R. (1961). A representation of the joint distribution of responses to n dichotomous items. In H. Solomon (Ed.), Studies on item analysis and prediction (pp. 158–168). Stanford: Stanford Mathematical Studies in the Social Sciences VI, Stanford University Press.

    Google Scholar 

  • Barnett, V. (2009). Comparative statistical inference (3rd ed.). New York: Wiley.

    Google Scholar 

  • Bartlett, M. (1957). A comment on D.V. Lindley’s statistical paradox. Biometrika44, 533–534.

    Google Scholar 

  • Bates, D. (2011). Computational methods for mixed models. Technical report, http://cran.r-project.org/web/packages/lme4/index.html.

  • Bates, D., & Watts, D. (1980). Curvature measures of nonlinearity (with discussion). Journal of the Royal Statistical Society, Series B42, 1–25.

    MathSciNet  MATH  Google Scholar 

  • Bates, D., & Watts, D. (1988). Nonlinear regression analysis and its applications. New York: Wiley.

    Book  MATH  Google Scholar 

  • Bauer, E., & Kohavi, R. (1999). An empirical comparison of voting classification algorithms: Bagging, boosting, and variants. Machine Learning36, 105–139.

    Article  Google Scholar 

  • Bayes, T. (1763). An essays towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London53, 370–418. Reprinted, with an introduction by George Barnard, in 1958 in Biometrika, 45, 293–315.

    Google Scholar 

  • Beal, S., & Sheiner, L. (1982). Estimating population kinetics. CRC Critical Reviews in Biomedical Engineering8, 195–222.

    Google Scholar 

  • Beale, E. (1960). Confidence regions in non-linear estimation (with discussion). Journal of the Royal Statistical Society, Series B22, 41–88.

    MathSciNet  MATH  Google Scholar 

  • Beaumont, M., Wenyang, Z., & Balding, D. (2002). Approximate Bayesian computation in population genetics. Genetics162, 2025–2035.

    Google Scholar 

  • Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, Series B, 57, 289–300.

    MathSciNet  MATH  Google Scholar 

  • Berger, J. (2003). Could Fisher, Jeffreys and Neyman have agreed on testing? (with discussion). Statistical Science18, 1–32.

    Article  MathSciNet  MATH  Google Scholar 

  • Berger, J. (2006). The case for objective Bayesian analysis. Bayesian Analysis1, 385–402.

    Article  MathSciNet  Google Scholar 

  • Berger, J., & Bernardo, J. (1992). On the development of reference priors (with discussion). In J. Bernardo, J. Berger, A. Dawid, & A. Smith (Eds.), Bayesian statistics 4, Proceedings of the Fourth Valencia International Meeting (pp. 35–60). Oxford: Oxford University Press.

    Google Scholar 

  • Berger, J. & Wolpert, R. (1988). The likelihood principle: A review, generalizations, and statistical implications. Hayward: IMS Lecture Notes.

    Google Scholar 

  • Berk, R. (2008). Statistical learning from a regression perspective. New York: Springer.

    MATH  Google Scholar 

  • Bernardo, J. (1979). Reference posterior distributions for Bayesian inference (with discussion). Journal of the Royal Statistical Society, Series B41, 113–147.

    MathSciNet  MATH  Google Scholar 

  • Bernardo, J., & Smith, A. (1994). Bayesian theory. New York: Wiley.

    Book  MATH  Google Scholar 

  • Bernstein, S. (1917). Theory of probability (Russian). Moscow-Leningrad: Gostekhizdat.

    Google Scholar 

  • Besag, J., & Kooperberg, C. (1995). On conditional and intrinsic auto-regressions. Biometrika, 82, 733–746.

    MathSciNet  MATH  Google Scholar 

  • Besag, J., York, J., & Mollié, A. (1991). Bayesian image restoration with two applications in spatial statistics. Annals of the Institute of Statistics and Mathematics43, 1–59.

    Article  MATH  Google Scholar 

  • Bickel, P., & Freedman, D. (1981). Some asymptotic theory for the bootstrap. Annals of Statistics9, 1196–1217.

    Article  MathSciNet  MATH  Google Scholar 

  • Bishop, Y., Feinberg, S., & Holland, P. (1975). Discrete multivariate analysis: Theory and practice. Cambridge: MIT.

    MATH  Google Scholar 

  • Black, D. (1984). Investigation of the possible increased incidence of cancer in West Cumbria. London: Report of the Independent Advisory Group, HMSO.

    Google Scholar 

  • Bliss, C. (1935). The calculation of the dosage-mortality curves. Annals of Applied Biology, 22, 134–167.

    Article  Google Scholar 

  • de Boor, C. (1978). A practical guide to splines. New York: Springer.

    Book  MATH  Google Scholar 

  • Bowman, A., & Azzalini, A. (1997). Applied smoothing techniques for data analysis. Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Breiman, L. (1996). Bagging predictors. Machine Learning24, 123–140.

    MathSciNet  MATH  Google Scholar 

  • Breiman, L. (2001a). Random forests. Machine Learning45, 5–32.

    Article  MATH  Google Scholar 

  • Breiman, L. (2001b). Statistical modeling: The two cultures (with discussion). Statistical Science16, 199–231.

    Article  MathSciNet  MATH  Google Scholar 

  • Breiman, L., & Spector, P. (1992). Submodel selection and evaluation in regression. the x-random case. International Statistical Review60, 291–319.

    Google Scholar 

  • Breiman, L., Friedman, J., Olshen, R., & Stone, C. (1984). Classification and regression trees. Monterrey: Wadsworth.

    MATH  Google Scholar 

  • Breslow, N. (2005). Whither PQL? In D. Lin & P. Heagerty (Eds.), Proceedings of the Second Seattle Symposium (pp. 1–22). New York: Springer.

    Google Scholar 

  • Breslow, N. & Chatterjee, N. (1999). Design and analysis of two-phase studies with binary outcome applied to Wilms tumour prognosis. Applied Statistics48, 457–468.

    Article  MATH  Google Scholar 

  • Breslow, N., & Clayton, D. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association88, 9–25.

    MATH  Google Scholar 

  • Breslow, N., & Day, N. (1980). Statistical methods in cancer research, Volume 1- The analysis of case-control studies. Lyon: IARC Scientific Publications No. 32.

    Google Scholar 

  • Brinkman, N. (1981). Ethanol fuel – a single-cylinder engine study of efficiency and exhaust emissions. SAE Transcations90, 1410–1424.

    Google Scholar 

  • Brooks, S., Gelman, A., Jones, G., & Meng, X.-L. (Eds.). (2011). Handbook of Markov chain Monte Carlo. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Bühlmann, P., & Yu, B. (2002). Analyzing bagging. The Annals of Statistics30, 927–961.

    Article  MathSciNet  MATH  Google Scholar 

  • Buja, A., Hastie, T., & Tibshirani, R. (1989). Linear smoothers and additive models (with discussion). Annals of Statistics17, 453–555.

    Article  MathSciNet  MATH  Google Scholar 

  • Buse, A. (1982). The likelihood ratio, Wald, and Lagrange multiplier tests: an expository note. The American Statistician36, 153–157.

    Google Scholar 

  • Cameron, A., & Trivedi, P. (1998). Regression analysis of count data. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  • Carey, V., Zeger, S., & Diggle, P. (1993). Modeling multivariate binary data with alternating logistic regressions. Biometrika80, 517–526.

    Article  MATH  Google Scholar 

  • Carlin, B., & Louis, T. (2009). Bayesian methods for data analysis (3rd ed.). Boca Raton: Chapman and Hall/CDC.

    Google Scholar 

  • Carroll, R., & Ruppert, D. (1988). Transformations and weighting in regression. Boca Raton: Chapman and Hall/CRC.

    Google Scholar 

  • Carroll, R., Ruppert, D., & Stefanski, L. (1995). Measurement error in nonlinear models. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Carroll, R., Rupert, D., Stefanski, L., & Crainiceanu, C. (2006). Measurement error in nonlinear models: A modern perspective (2nd ed.). Boca Raton: Chapman and Hall/CRC.

    Book  MATH  Google Scholar 

  • Casella, G., & Berger, R. (1987). Reconciling Bayesian evidence in the one-sided testing problem. Journal of the American Statistical Association82, 106–111.

    Article  MathSciNet  MATH  Google Scholar 

  • Casella, G., & Berger, R. (1990). Statistical inference. Pacific Grove: Wadsworth and Brooks.

    MATH  Google Scholar 

  • Chaloner, K., & Brant, R. (1988). A Bayesian approach to outlier detection and residual analysis. Biometrika75, 651–659.

    Article  MathSciNet  MATH  Google Scholar 

  • Chambers, R., & Skinner, C. (2003). Analysis of survey data. New York: Wiley.

    Book  MATH  Google Scholar 

  • Chan, K., & Geyer, C. (1994). Discussion of “Markov chains for exploring posterior distributions”. The Annals of Statistics22, 1747–1758.

    Article  Google Scholar 

  • Chatfield, C. (1995). Model uncertainty, data mining and statistical inference (with discussion). Journal of the Royal Statistical Society, Series A158, 419–466.

    Article  Google Scholar 

  • Chaudhuri, P., & Marron, J. (1999). SiZer for exploration of structures in curves. Journal of the American Statistical Association94, 807–823.

    Article  MathSciNet  MATH  Google Scholar 

  • Chen, S., Donoho, D., & Saunders, M. (1998). Atomic decomposition by basis pursuit. SIAM Journal of Scientific Computing20, 33–61.

    Article  MathSciNet  Google Scholar 

  • Chipman, H., George, E., & McCulloch, R. (1998). Bayesian cart model search (with discussion). Journal of the American Statistical Association93, 935–960.

    Article  Google Scholar 

  • Clayton, D., & Hills, M. (1993). Statistical models in epidemiology. Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Clayton, D., & Kaldor, J. (1987). Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics43, 671–682.

    Article  Google Scholar 

  • Cleveland, W., Grosse, E., & Shyu, W. (1991). Local regression models. In J. Chambers & T. Hastie (Eds.), Statistical models in S (pp. 309–376). Pacific Grove: Wadsworth and Brooks/Cole.

    Google Scholar 

  • Cochran, W. (1977). Sampling techniques. New York: Wiley.

    MATH  Google Scholar 

  • Cook, R., & Weisberg, S. (1982). Residuals and influence in regression. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Cox, D. (1972). The analysis of multivariate binary data. Journal of the Royal Statistical Society, Series C21, 113–120.

    Article  Google Scholar 

  • Cox, D. (1983). Some remarks on overdispersion. Biometrika70, 269–274.

    Article  MathSciNet  MATH  Google Scholar 

  • Cox, D. (2006). Principles of statistical inference. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Cox, D., & Hinkley, D. (1974). Theoretical statistics. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Cox, D., & Reid, N. (2000). The theory of the design of experiments. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Cox, D., & Snell, E. (1989). The analysis of binary data (2nd ed.). Boca Raton: Chapman and Hall/CRC.

    Google Scholar 

  • Craig, P., Goldstein, M., Seheult, A., & Smith, J. (1998). Constructing partial prior specifications for models of complex physical systems. Journal of the Royal Statistical Society, Series D, 47, 37–53.

    Article  Google Scholar 

  • Crainiceanu, C., Ruppert, D., & Wand, M. (2005). Bayesian analysis for penalized spline regression using WinBUGS. Journal of Statistical Software14, 1–24.

    Google Scholar 

  • Craven, P., & Wabha, G. (1979). Smoothing noisy data with spline functions. Numerische Mathematik31, 377–403.

    Article  MATH  Google Scholar 

  • Crowder, M. (1986). On consistency and inconsistency of estimating equations. Econometric Theory2, 305–330.

    Article  Google Scholar 

  • Crowder, M. (1987). On linear and quadratic estimating functions. Biometrika74, 591–597.

    Article  MathSciNet  MATH  Google Scholar 

  • Crowder, M. (1995). On the use of a working correlation matrix in using generalized linear models for repeated measures. Biometrika82, 407–410.

    Article  MATH  Google Scholar 

  • Crowder, M., & Hand, D. (1990). Analysis of repeated measures. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Crowder, M., & Hand, D. (1996). Practical longitudinal data analysis. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Darby, S., Hill, D., & Doll, R. (2001). Radon: a likely carcinogen at all exposures. Annals of Oncology12, 1341–1351.

    Article  Google Scholar 

  • Darroch, J., Lauritzen, S., & Speed, T. (1980). Markov fields and log-linear interaction models for contingency tables. The Annals of Statistics8, 522–539.

    Article  MathSciNet  MATH  Google Scholar 

  • Davidian, M., & Giltinan, D. (1995). Nonlinear models for repeated measurement data. Boca Raton: Chapman and Hall/CRC.

    Google Scholar 

  • Davies, O. (1967). Statistical methods in research and production (3rd ed.). London: Olive and Boyd.

    Google Scholar 

  • Davison, A. (2003). Statistical models. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Davison, A., & Hinkley, D. (1997). Bootstrap methods and their application. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  • De Finetti, B. (1974). Theory of probability, volume 1. New York: Wiley.

    Google Scholar 

  • De Finetti, B. (1975). Theory of probability, volume 2. New York: Wiley.

    Google Scholar 

  • Demidenko, E. (2004). Mixed models. Theory and applications. New York: Wiley.

    Book  MATH  Google Scholar 

  • Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society, Series B39(1), 1–38.

    MathSciNet  MATH  Google Scholar 

  • Denison, D., & Holmes, C. (2001). Bayesian partitioning for estimating disease risk. Biometrics57, 143–149.

    Article  MathSciNet  MATH  Google Scholar 

  • Denison, D., Holmes, C., Mallick, B., & Smith, A. (2002). Bayesian methods for nonlinear classification and regression. New York: Wiley.

    MATH  Google Scholar 

  • Dennis, J., Jr, & Schnabel, R. (1996). Numerical methods for unconstrained optimization and nonlinear equations. Englewood Cliffs: Siam.

    Book  MATH  Google Scholar 

  • Devroye, L. (1986). Non-uniform random variate generation. New York: Springer.

    MATH  Google Scholar 

  • Diaconis, P., & Freedman, D. (1986). On the consistency of Bayes estimates. Annals of Statistics14, 1–26.

    Article  MathSciNet  MATH  Google Scholar 

  • Diaconis, P., & Ylvisaker, D. (1980). Quantifying prior opinion (with discussion). In J. Bernardo, M. D. Groot, D. Lindley, & A. Smith (Eds.), Bayesian statistics 2 (pp. 133–156). Amsterdam: North Holland.

    Google Scholar 

  • DiCiccio, T., Kass, R., Raftery, A., & Wasserman, L. (1997). Computing Bayes factors by combining simulation and asymptotic approximations. Journal of the American Statistical Association92, 903–915.

    Article  MathSciNet  MATH  Google Scholar 

  • Diggle, P., & Rowlingson, B. (1994). A conditional approach to point process modelling of raised incidence. Journal of the Royal Statistical Society, Series A157, 433–440.

    Article  Google Scholar 

  • Diggle, P., Morris, S., & Wakefield, J. (2000). Point source modelling using matched case-control data. Biostatistics1, 89–105.

    Article  MATH  Google Scholar 

  • Diggle, P., Heagerty, P., Liang, K.-Y., & Zeger, S. (2002). Analysis of longitudinal data (2nd ed.). Oxford: Oxford University Press.

    Google Scholar 

  • Doob, J. (1948). Le Calcul des Probabilités et ses Applications, Chapter Application of the theory of martingales (pp. 22–28). Colloques Internationales du CNRS Paris.

    Google Scholar 

  • Duchon, J. (1977). Splines minimizing rotation-invariant semi-norms in Solobev spaces. In W. Schemp & K. Zeller (Eds.), Construction theory of functions of several variables (pp. 85–100). New York: Springer.

    Chapter  Google Scholar 

  • Dwyer, J., Andrews, E., Berkey, C., Valadian, I., & Reed, R. (1983). Growth in “new” vegetarian preschool children using the Jenss-Bayley curve fitting technique. American Journal of Clinical Nutrition37, 815–827.

    Google Scholar 

  • Efron, B. (1975). The efficiency of logistic regression compared to normal discriminant analysis. Journal of the American Statistical Association70, 892–898.

    Article  MathSciNet  MATH  Google Scholar 

  • Efron, B. (1979). Bootstrap methods: Another look at the jacknife. Annals of Statistics7, 1–26.

    Article  MathSciNet  MATH  Google Scholar 

  • Efron, B. (2008). Microarrays, empirical Bayes and the two groups model (with discussion). Statistical Science23, 1–47.

    Article  MathSciNet  Google Scholar 

  • Efron, B., & Tibshirani, R. (1993). An introduction to the bootstrap. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Efroymson, M. (1960). Multiple regression analysis. In A. Ralston & H. Wilf (Eds.), Mathematical methods for digital computers (pp. 191–203). New YOrk: Wiley.

    Google Scholar 

  • Eilers, P., & Marx, B. (1996). Flexible smoothing with B-splines and penalties. Statistical Science11, 89–102.

    Article  MathSciNet  MATH  Google Scholar 

  • Essenberg, J. (1952). Cigarette smoke and the incidence of primary neoplasm of the lung in the albino mouse. Science116, 561–562.

    Article  Google Scholar 

  • Evans, M., & Swartz, T. (2000). Approximating integrals via Monte Carlo and deterministic methods. Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Fan, J. (1992). Design-adaptive nonparametric regression. Journal of the American Statistical Association87, 1273–1294.

    Article  Google Scholar 

  • Fan, J. (1993). Local linear regression smoothers and their minimax efficiencies. Annals of Statistics21, 196–215.

    Article  MathSciNet  MATH  Google Scholar 

  • Fan, J. & I. Gijbels (1996). Local polynomial modelling and its applications. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Faraway, J. (2004). Linear models with R. Boca Raton: Chapman and Hall/CRC.

    Google Scholar 

  • Fearnhead, P., & Prangle, D. (2012). Constructing summary statistics for approximate bayesian computation: semi-automatic approximate bayesian computation (with discussion). Journal of the Royal Statistical Society, Series B74, 419–474.

    Article  MathSciNet  Google Scholar 

  • Ferguson, T. (1996). A course in large sample theory. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Feynman, R. (1951). The concept of probability in quantum mechanics. In J. Neyman (Ed.), Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (pp. 535–541). California: University of California Press.

    Google Scholar 

  • Fine, P., Ponnighaus, J., Maine, N., Clarkson, J., & Bliss, L. (1986). Protective efficacy of BCG against leprosy in Northern Malawi. The Lancet328, 499–502.

    Article  Google Scholar 

  • Firth, D. (1987). On the efficiency of quasi-likelihood estimation. Biometrika74, 233–245.

    Article  MathSciNet  MATH  Google Scholar 

  • Firth, D. (1993). Recent developments in quasi-likelihood methods. In Bulletin of the international Statistical Institute, 55, 341–358.

    Google Scholar 

  • Fisher, R. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London, Series A222, 309–368.

    Article  MATH  Google Scholar 

  • Fisher, R. (1925a). Statistical methods for research workers. Edinburgh: Oliver and Boyd.

    Google Scholar 

  • Fisher, R. (1925b). Theory of statistical estimation. Proceedings of the Cambridge Philosophical Society22, 700–725.

    Article  MATH  Google Scholar 

  • Fisher, R. (1935). The logic of inductive inference (with discussion). Journal of the Royal Statistical Society, Series A98, 39–82.

    Google Scholar 

  • Fisher, R. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7, 179–188.

    Google Scholar 

  • Fisher, R. (1990). Statistical methods, experimental design and scientific inference. Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Fitzmaurice, G., & Laird, N. (1993). A likelihood-based method for analyzing longitudinal binary responses. Biometrika80, 141–151.

    Article  MATH  Google Scholar 

  • Fitzmaurice, G., Laird, N., & Rotnitzky, A. (1993). Regression models for discrete longitudinal responses (with discussion). Statistical Science8, 248–309.

    MathSciNet  Google Scholar 

  • Fitzmaurice, G., Laird, N., & Ware, J. (2004). Applied longitudinal analysis. New York: Wiley.

    MATH  Google Scholar 

  • Fong, Y., Rue, H., & Wakefield, J. (2010). Bayesian inference for generalized linear models. Biostatistics11, 397–412.

    Article  Google Scholar 

  • Freedman, D. (1997). From association to causation via regression. Advances in Applied Mathematics18, 59–110.

    Article  MathSciNet  MATH  Google Scholar 

  • Freund, Y., & Schapire, R. (1997). Experiments with a new boosting algorithm. In Machine Learning: Proceedings for the Thirteenth International Conference, San Fransisco (pp. 148–156). Los Altos: Morgan Kaufmann.

    Google Scholar 

  • Friedman, J. (1979). A tree-structured approach to nonparametric multiple regression. In T. Gasser & M. Rosenblatt (Eds.), Smoothing techniques for curve estimation (pp. 5–22). New York: Springer.

    Chapter  Google Scholar 

  • Friedman, J. (1991). Multivariate adaptive regression splines (with discussion). Annals of Statistics19, 1–141.

    Article  MathSciNet  MATH  Google Scholar 

  • Friedman, J., Hastie, T., & Tibshirani, R. (2000). Additive logistic regression: A statistical view of boosting (with discussion). Annals of Statistics28, 337–407.

    Article  MathSciNet  MATH  Google Scholar 

  • Gallant, A. (1987). Nonlinear statistical models. New York: Wiley.

    Book  MATH  Google Scholar 

  • Gamerman, D. and Lopes, H. F. (2006). Markov chain Monte Carlo: Stochastic simulation for Bayesian inference (2nd ed.). Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Gasser, T., Stroka, L., & Jennen-Steinmetz, C. (1986). Residual variance and residual pattern in nonlinear regression. Biometrika73, 625–633.

    Article  MathSciNet  MATH  Google Scholar 

  • Gelfand, A. E., Diggle, P. J., Fuentes, M., & Guttorp, P. (Eds.). (2010). Handbook of spatial statistics. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models. Bayesian Analysis1, 515–534.

    Article  MathSciNet  Google Scholar 

  • Gelman, A., & Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge: Cambridge University Press.

    Google Scholar 

  • Gelman, A., & Rubin, D. (1992). Inference from iterative simulation using multiple sequences. Statistical Science7, 457–511.

    Article  Google Scholar 

  • Gelman, A., Carlin, J., Stern, H., & Rubin, D. (2004). Bayesian data analysis (2nd ed.). Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Gibaldi, M., & Perrier, D. (1982). Pharmacokinetics (2nd ed.). New York: Marcel Dekker.

    Google Scholar 

  • Giné, E., Götze, F., & Mason, D. (1997). When is the Student t-statistic asymptotically normal? The Annals of Probability25, 1514–1531.

    Article  MathSciNet  MATH  Google Scholar 

  • Glynn, P., & Iglehart, D. (1990). Simulation output using standardized time series. Mathematics of Operations Research15, 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  • Gneiting, T., & Raftery, A. (2007). Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association102, 359–378.

    Article  MathSciNet  MATH  Google Scholar 

  • Godambe, V., & Heyde, C. (1987). Quasi-likelihood and optimal estimation. International Statistical Review55, 231–244.

    Article  MathSciNet  MATH  Google Scholar 

  • Godfrey, K. (1983). Compartmental models and their applications. London: Academic.

    Google Scholar 

  • Goldstein, M., & Wooff, D. (2007). Bayes linear statistics, theory and methods. New York: Wiley.

    Book  MATH  Google Scholar 

  • Golub, G., Heath, M. & Wabha, G. (1979). Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics21, 215–223.

    Article  MathSciNet  MATH  Google Scholar 

  • Goodman, S. (1993). p values, hypothesis tests and likelihood: Implications for epidemiology of a neglected historical debate. American Journal of Epidemiology137, 485–496.

    Google Scholar 

  • Gordon, L., & Olshen, R. A. (1978). Asymptotically efficient solutions to the classification problems. Annals of Statistics6, 515–533.

    Article  MathSciNet  MATH  Google Scholar 

  • Gordon, L., & Olshen, R. A. (1984). Almost surely consistent nonparametric regression from recursive partitioning schemes. Journal of Multivariate Analysis15, 147–163.

    Article  MathSciNet  MATH  Google Scholar 

  • Gourieroux, C., Montfort, A., & Trognon, A. (1984). Pseudo-maximum likelihood methods: Theory. Econometrica52, 681–700.

    Article  MathSciNet  MATH  Google Scholar 

  • Green, P., & Silverman, B. (1994). Nonparametric regression and generalized linear models. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Green, P. J. (1995). Reversible jump MCMC computation and Bayesian model determination. Biometrika82, 711–732.

    Article  MathSciNet  MATH  Google Scholar 

  • Greenland, S., Robins, J., & Pearl, J. (1999). Confounding and collapsibility in causal inference. Statistical Science14, 29–46.

    Article  MATH  Google Scholar 

  • Gu, C. (2002). Smoothing spline ANOVA models. New York: Springer.

    MATH  Google Scholar 

  • Haberman, S. (1977). Maximum likelihood estimates in exponential response models. Annals of Statistics5, 815–841.

    Article  MathSciNet  MATH  Google Scholar 

  • Hand, D. and Crowder, M. (1991). Practical longitudinal data analysis. Boca Raton: Chapman and Hall/CRC Press.

    Google Scholar 

  • Haldane, J. (1948). The precision of observed values of small frequencies. Biometrika35, 297–303.

    MathSciNet  Google Scholar 

  • Härdle, W., Hall, P., & Marron, J. (1988). How far are automatically chosen smoothing parameters from their optimum? Journal of the American Statistical Association83, 86–101.

    MathSciNet  MATH  Google Scholar 

  • Hastie, T., & Tibshirani, R. (1990). Generalized additive models. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Hastie, T., & Tibshirani, R. (1993). Varying-coefficient models. Journal of the Royal Statistical Society, Series B55, 757–796.

    MathSciNet  MATH  Google Scholar 

  • Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning (2nd ed.). New York: Springer.

    Book  MATH  Google Scholar 

  • Hastings, W. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika57, 97–109.

    Article  MATH  Google Scholar 

  • Haughton, D. (1988). On the choice of a model to fit data from an exponential family. The Annals of Statistics16, 342–355.

    Article  MathSciNet  MATH  Google Scholar 

  • Haughton, D. (1989). Size of the error in the choice of a model to fit from an exponential family. Sankhya: The Indian Journal of Statistics, Series A51, 45–58.

    MathSciNet  MATH  Google Scholar 

  • Heagerty, P., Kurland, B. (2001). Misspecified maximum likelihood estimates and generalised linear mixed models. Biometrika88, 973–986.

    Article  MathSciNet  MATH  Google Scholar 

  • Heyde, C. (1997). Quasi-likelihood and its applications. New York: Springer.

    Book  Google Scholar 

  • Hobert, J., & Casella, G. (1996). The effect of improper priors on Gibbs sampling in hierarchical linear mixed models. Journal of the American Statistical Association91, 1461–1473.

    Article  MathSciNet  MATH  Google Scholar 

  • Hodges, J., & Reich, B. (2010). Adding spatially-correlated errors can mess up the fixed effect you love. The American Statistician64, 325–334.

    Article  MathSciNet  MATH  Google Scholar 

  • Hoerl, A., & Kennard, R. (1970). Ridge regression: Biased estimation for non-orthogonal problems. Technometrics12, 55–67.

    Article  MATH  Google Scholar 

  • Hoff, P. (2009). A first course in Bayesian statistical methods. New York: Springer.

    Book  MATH  Google Scholar 

  • Holst, U., Hössjer, O., Björklund, C., Ragnarson, P., & Edner, H. (1996). Locally weighted least squares kernel regression and statistical evaluation of LIDAR measurements. Environmetrics, 7, 401–416.

    Article  Google Scholar 

  • Hothorn, T., Hornik, K., & Zeileis, A. (2006). Unbiased recursive partitioning: A conditional inference framework. Journal of Computational and Graphical Statistics15, 651–674.

    Article  MathSciNet  Google Scholar 

  • Huber, P. (1967). The behavior of maximum likelihood estimators under non-standard conditions. In L. LeCam & J. Neyman (Eds.), Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (pp. 221–233). California: University of California Press.

    Google Scholar 

  • Inoue, L., & Parmigiani, G. (2009). Decision theory: Principles and approaches. New York: Wiley.

    MATH  Google Scholar 

  • Izenman, A. (2008). Modern multivariate statistical techniques: Regression, classification, and manifold learning. New York: Springer.

    MATH  Google Scholar 

  • Jeffreys, H. (1961). Theory of probability (3rd ed.). Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Jenss, R., & Bayley, N. (1937). A mathematical method for studying the growth of a child. Human Biology9, 556–563.

    Google Scholar 

  • Johnson, N., Kotz, S., & Balakrishnan, N. (1994). Continuous univariate distributions, volume 1 (2nd ed.). New York: Wiley.

    Google Scholar 

  • Johnson, N., Kotz, S., & Balakrishnan, N. (1995). Continuous univariate distributions, volume 2 (2nd ed.). New York: Wiley.

    Google Scholar 

  • Johnson, N., Kotz, S., & Balakrishnan, N. (1997). Discrete multivariate distributions. New York: Wiley.

    MATH  Google Scholar 

  • Johnson, N., Kemp, A., & Kotz, S. (2005). Univariate discrete distributions (3rd ed.). New York: Wiley.

    Book  MATH  Google Scholar 

  • Johnson, V. (2008). Bayes factors based on test statistics. Journal of the Royal Statistical Society, Series B67, 689–701.

    Google Scholar 

  • Jordan, M., Ghahramani, Z., Jaakkola, T., & Saul, L. (1999). An introduction to variational methods for graphical models. Machine Learning37, 183–233.

    Article  MATH  Google Scholar 

  • Kadane, J., & Wolfson, L. (1998). Experiences in elicitation. Journal of the Royal Statistical Society, Series D47, 3–19.

    Article  Google Scholar 

  • Kalbfleisch, J., & Prentice, R. (2002). The statistical analysis of failure time data (2nd ed.). New York: Wiley.

    Book  MATH  Google Scholar 

  • Kass, R., & Raftery, A. (1995). Bayes factors. Journal of the American Statistical Association90, 773–795.

    Article  MATH  Google Scholar 

  • Kass, R., & Vaidyanathan, S. (1992). Approximate Bayes factors and orthogonal parameters, with application to testing equality of two binomial proportions. Journal of the Royal Statistical Society, Series B54, 129–144.

    MathSciNet  MATH  Google Scholar 

  • Kass, R., Tierney, L., & Kadane, J. (1990). The validity of posterior expansions based on Laplace’s method. In S. Geisser, J. Hodges, S. Press, & A. Zellner (Eds.), Bayesian and likelihood methods in statistics and econometrics (pp. 473–488). Amsterdam: North-Holland.

    Google Scholar 

  • Kauermann, G. (2005). A note on smoothing parameter selection for penalized spline smoothing. Journal of Statistical Planning and Inference127, 53–69.

    Article  MathSciNet  MATH  Google Scholar 

  • Kauermann, G., & Carroll, R. (2001). A note on the efficiency of sandwich covariance matrix estimation. Journal of the American Statistical Association96, 1387–1396.

    Article  MathSciNet  MATH  Google Scholar 

  • Kemp, I., Boyle, P., Smans, M., & Muir, C. (1985). Atlas of cancer in Scotland, 1975–1980: Incidence and epidemiologic perspective. Lyon: IARC Scientific Publication No. 72.

    Google Scholar 

  • Kerr, K. (2009). Comments on the analysis of unbalanced microarray data. Bioinformatics25, 2035–2041.

    Article  Google Scholar 

  • Kim, H., & Loh, W.-Y. (2001). Classification trees with unbiased multiway splits. Journal of the American Statistical Association96, 589–604.

    Article  MathSciNet  Google Scholar 

  • Knafl, G., Sacks, J., & Ylvisaker, D. (1985). Confidence bands for regression functions. Journal of the American Statistical Association80, 683–691.

    Article  MathSciNet  MATH  Google Scholar 

  • Knorr-Held, L., & Rasser, G. (2000). Bayesian detection of clusters and discontinuities in disease maps. Biometrics56, 13–21.

    Article  MATH  Google Scholar 

  • Korn, E., & Graubard, B. (1999). Analysis of health surveys. New York: Wiley.

    Book  MATH  Google Scholar 

  • Kosorok, M. (2008). Introduction to empirical processes and semiparametric inference. New York: Springer.

    Book  MATH  Google Scholar 

  • Kotz, S., Balakrishnan, N., & Johnson, N. (2000). Continuous multivariate distributions, volume 1 (2nd ed.). New York: Wiley.

    Book  Google Scholar 

  • Laird, N., & Ware, J. (1982). Random-effects models for longitudinal data. Biometrics38, 963–974.

    Article  MATH  Google Scholar 

  • Lange, N., & Ryan, L. (1989). Assessing normality in random effects models. Annals of Statistics17, 624–642.

    Article  MathSciNet  MATH  Google Scholar 

  • Lehmann, E. (1986). Testing statistical hypotheses (2nd ed.). New York: Wiley.

    MATH  Google Scholar 

  • Lehmann, E., & Romano, J. (2005). Generalizations of the familywise error rate. Annals of Statistics33, 1138–1154.

    Article  MathSciNet  MATH  Google Scholar 

  • van der Lende, R., Kok, T., Peset, R., Quanjer, P., Schouten, J., & Orie, N. G. (1981). Decreases in VC and FEV1 with time: Indicators for effects of smoking and air pollution. Bulletin of European Physiopathology and Respiration17, 775–792.

    Google Scholar 

  • Liang, K., & Zeger, S. (1986). Longitudinal data analysis using generalized linear models. Biometrika73, 13–22.

    Article  MathSciNet  MATH  Google Scholar 

  • Liang, K.-Y., & McCullagh, P. (1993). Case studies in binary dispersion. Biometrics49, 623–630.

    Article  Google Scholar 

  • Liang, K.-Y., Zeger, S., & Qaqish, B. (1992). Multivariate regression analyses for categorical data (with discussion). Journal of the Royal Statistical Society, Series B54, 3–40.

    MathSciNet  MATH  Google Scholar 

  • Lindley, D. (1957). A statistical paradox. Biometrika44, 187–192.

    MathSciNet  MATH  Google Scholar 

  • Lindley, D. (1968). The choice of variables in multiple regression (with discussion). Journal of the Royal Statistical Society, Series B30, 31–66.

    MathSciNet  MATH  Google Scholar 

  • Lindley, D. (1980). Approximate Bayesian methods. In J. Bernardo, M. D. Groot, D. Lindley, & A. Smith (Eds.), Bayesian statistics (pp. 223–237). Valencia: Valencia University Press.

    Google Scholar 

  • Lindley, D., & Smith, A. (1972). Bayes estimates for the linear model (with discussion). Journal of the Royal Statistical Society, Series B34, 1–41.

    MathSciNet  MATH  Google Scholar 

  • Lindsey, J., Byrom, W., Wang, J., Jarvis, P., & Jones, B. (2000). Generalized nonlinear models for pharmacokinetic data. Biometrics56, 81–88.

    Article  MATH  Google Scholar 

  • Lindstrom, M., & Bates, D. (1990). Nonlinear mixed-effects models for repeated measures data. Biometrics46, 673–687.

    Article  MathSciNet  Google Scholar 

  • Lipsitz, S., Laird, N., & Harrington, D. (1991). Generalized estimating equations for correlated binary data: Using the odds ratio as a measure of association. Biometrika78, 153–160.

    Article  MathSciNet  Google Scholar 

  • Little, R., & Rubin, D. (2002). Statistical analysis with missing data (2nd ed.). New York: Wiley.

    MATH  Google Scholar 

  • Loader, C. (1999). Local regression and likelihood. New York: Springer.

    MATH  Google Scholar 

  • Lumley, T. (2010). Complex surveys: A guide to analysis using R. New York: Wiley.

    Google Scholar 

  • Lumley, T., Diehr, P., Emerson, S., & Chen, L. (2002). The importance of the normality assumption in large public health data sets. Annual Reviews of Public Health23, 151–169.

    Article  Google Scholar 

  • Machin, D., Farley, T., Busca, B., Campbell, M., & d’Arcangues, C. (1988). Assessing changes in vaginal bleeding patterns in contracepting women. Contraception38, 165–179.

    Google Scholar 

  • Malahanobis, P. (1936). On the generalised distance in statistics. Proceedings of the National Institute of Sciences of India2, 49–55.

    Google Scholar 

  • Mallows, C. (1973). Some comments on C p . Technometrics15, 661–667.

    MATH  Google Scholar 

  • Marra, G., & Wood, S. (2012). Coverage properties of confidence intervals for generalized additive model components. Scandinavian Journal of Statistics39, 53–74.

    Article  MathSciNet  MATH  Google Scholar 

  • van Marter, L., Leviton, A., Kuban, K., Pagano, M., & Allred, E. (1990). Maternal glucocorticoid therapy and reduced risk of bronchopulmonary dysplasia. Pediatrics86, 331–336.

    Google Scholar 

  • Matheron, G. (1971). The theory of regionalized variables and its applications. Technical report, Les Cahiers du Centre de Morphologie Mathématique de Fontainebleau, Fascicule 5, Ecole des Mines de Paris.

    Google Scholar 

  • McCullagh, P. (1983). Quasi-likelihood functions. The Annals of Statistics11, 59–67.

    Article  MathSciNet  MATH  Google Scholar 

  • McCullagh, P., & Nelder, J. (1989). Generalized linear models (2nd ed.). Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • McCulloch, C., & Neuhaus, J. (2011). Prediction of random effects in linear and generalized linear models under model misspecification. Biometrics67, 270–279.

    Article  MathSciNet  MATH  Google Scholar 

  • McDonald, B. (1993). Estimating logistic regression parameters for bivariate binary data. Journal of the Royal Statistical Society, Series B55, 391–397.

    MATH  Google Scholar 

  • Meier, L., van de Geer, S., & Bühlmann, P. (2008). The group lasso for logistic regression. Journal of the Royal Statistical Society, Series B70, 53–71.

    Article  MATH  Google Scholar 

  • Meinshausen, N., & Yu, B. (2009). Lasso-type recovery of sparse representations for high-dimensional data. The Annals of Statistics37, 246–270.

    Article  MathSciNet  MATH  Google Scholar 

  • Mendel, G. (1866). Versuche über Pflanzen-Hybriden. Verhandl d Naturfsch Ver in Bünn4, 3–47.

    Google Scholar 

  • Mendel, G. (1901). Experiments in plant hybridization. Journal of the Royal Horticultural Society26, 1–32. Translation of Mendel (1866) by W. Bateson.

    Google Scholar 

  • Meng, X., & Wong, W. (1996). Simulating ratios of normalizing constants via a simple identity. Statistical Sinica6, 831–860.

    MathSciNet  MATH  Google Scholar 

  • Metropolis, N., Rosenbluth, A., Teller, A., & Teller, E. (1953). Equations of state calculations by fast computing machines. Journal of Chemical Physics21, 1087–1091.

    Article  Google Scholar 

  • Miller, A. (1990). Subset selection in regression. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • von Mises, R. (1931). Wahrscheinlichkeitsrecheung. Leipzig: Franz Deutiche.

    Google Scholar 

  • Montgomery, D., & Peck, E. (1982). Introduction to linear regression analysis. New York: Wiley.

    MATH  Google Scholar 

  • Morgan, J., & Messenger, R. (1973). Thaid: a sequential search program for the analysis of nominal scale dependent variables. Technical report, Ann Arbor: Institute for Social Research, University of Michigan.

    Google Scholar 

  • Morgan, J., & Sonquist, J. (1963). Problems in the analysis of survey data, and a proposal. Journal of the American Statistical Association58, 415–434.

    Article  MATH  Google Scholar 

  • Nadaraya, E. (1964). On estimating regression. Theory of Probability and its Applications9, 141–142.

    Article  Google Scholar 

  • Naylor, J., & Smith, A. (1982). Applications of a method for the efficient computation of posterior distributions. Applied Statistics31, 214–225.

    Article  MathSciNet  MATH  Google Scholar 

  • Neal, R. (1996). Bayesian learning for neural networks. New York: Springer.

    Book  MATH  Google Scholar 

  • Nelder, J. (1966). Inverse polynomials, a useful group of multi-factor response functions. Biometrics22, 128–141.

    Article  Google Scholar 

  • Nelder, J. A., & Wedderburn, R. W. M. (1972). Generalized linear models. Journal of the Royal Statistical Society, Series A135, 370–384.

    Article  Google Scholar 

  • Neyman, J., & Pearson, E. (1928). On the use and interpretation of certain test criteria for purposes of statistical inference. Part i. Philosophical Transactions of the Royal Society of London, Series A20A, 175–240.

    Google Scholar 

  • Neyman, J., & Pearson, E. (1933). On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London, Series A231, 289–337.

    Article  Google Scholar 

  • Neyman, J., & Scott, E. (1948). Consistent estimates based on partially consistent observations. Econometrica16, 1–32.

    Article  MathSciNet  Google Scholar 

  • Nychka, D. (1988). Bayesian confidence intervals for smoothing splines. Journal of the American Statistical Association83, 1134–1143.

    Article  MathSciNet  Google Scholar 

  • O’Hagan, A. (1994). Kendall’s advanced theory of statistics, volume 2B: Bayesian inference. London: Arnold.

    Google Scholar 

  • O’Hagan, A. (1998). Eliciting expert beliefs in substantial practical applications. Journal of the Royal Statistical Society, Series D47, 21–35.

    Article  Google Scholar 

  • O’Hagan, A., & Forster, J. (2004). Kendall’s advanced theory of statistics, volume 2B: Bayesian inference (2nd ed.). London: Arnold.

    MATH  Google Scholar 

  • Olshen, R. (2007). Tree-structured regression and the differentiation of integrals. Annals of Statistics35, 1–12.

    Article  MathSciNet  MATH  Google Scholar 

  • Ormerod, J., & Wand, M. (2010). Explaining variational approximations. The American Statistician64, 140–153.

    Article  MathSciNet  MATH  Google Scholar 

  • O’Sullivan, F. (1986). A statistical perspective on ill-posed problems. Statistical Science1, 502–518.

    Article  MathSciNet  MATH  Google Scholar 

  • Pagano, M., & Gauvreau, K. (1993). Principles of biostatistics. Belmont: Duxbury Press.

    Google Scholar 

  • Pearl, J. (2009). Causality: Models, reasoning and inference (2nd ed.). Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  • Pearson, E. (1953). Discussion of “Statistical inference” by D.V. Lindley. Journal of the Royal Statistical Society, Series B15, 68–69.

    Google Scholar 

  • Peers, H. (1971). Likelihood ratio and associated test criteria. Biometrika58, 577–587.

    Article  MATH  Google Scholar 

  • Pepe, M. (2003). The statistical evaluation of medical tests for classification and prediction. Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Pérez, J. M., & Berger, J. O. (2002). Expected-posterior prior distributions for model selection. Biometrika89, 491–512.

    Article  MathSciNet  MATH  Google Scholar 

  • Pinheiro, J., & Bates, D. (2000). Mixed-effects models in S and splus. New York: Springer.

    Book  Google Scholar 

  • Plummer, M. (2008). Penalized loss functions for Bayesian model comparison. Biostatistics9, 523–539.

    Article  MATH  Google Scholar 

  • Potthoff, R., & Roy, S. (1964). A generalized multivariate analysis of variance useful especially for growth curve problems. Biometrika51, 313–326.

    MathSciNet  MATH  Google Scholar 

  • Prentice, R. (1988). Correlated binary regression with covariates specific to each binary observation. Biometrics44, 1033–1048.

    Article  MathSciNet  MATH  Google Scholar 

  • Prentice, R., & Pyke, R. (1979). Logistic disease incidence models and case-control studies. Biometrika66, 403–411.

    Article  MathSciNet  MATH  Google Scholar 

  • Prentice, R., & Zhao, L. (1991). Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses. Biometrics47, 825–839.

    Article  MathSciNet  MATH  Google Scholar 

  • Qaqish, B., & Ivanova, A. (2006). Multivariate logistic models. Biometrika93, 1011–1017.

    Article  MathSciNet  Google Scholar 

  • Radelet, M. (1981). Racial characteristics and the imposition of the death sentence. American Sociological Review46, 918–927.

    Article  Google Scholar 

  • Rao, C. (1948). Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Proceedings of the Cambridge Philosophical Society44, 50–57.

    Article  MATH  Google Scholar 

  • Rao, C., & Wu, Y. (1989). A strongly consistent procedure for model selection in a regression problem. Biometrika76, 369–374.

    Article  MathSciNet  MATH  Google Scholar 

  • Rasmussen, C., & Williams, C. (2006). Gaussian processes for machine learning. Cambridge: MIT.

    MATH  Google Scholar 

  • Ravishanker, N., & Dey, D. (2002). A first course in linear model theory. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Reinsch, C. (1967). Smoothing by spline functions. Numerische Mathematik10, 177–183.

    Article  MathSciNet  MATH  Google Scholar 

  • Reiss, P., & Ogden, R. (2009). Smoothing parameter selection for a class of semiparametric linear models. Journal of the Royal Statistical Society, Series B71, 505–523.

    Article  MathSciNet  MATH  Google Scholar 

  • Rice, J. (1984). Bandwidth choice for nonparametric regression. Annals of Statistics12, 1215–1230.

    Article  MathSciNet  MATH  Google Scholar 

  • Rice, K. (2008). Equivalence between conditional and random-effects likelihoods for pair-matched case-control studies. Journal of the American Statistical Association103, 385–396.

    Article  MathSciNet  MATH  Google Scholar 

  • Ripley, B. (1987). Stochastic simulation. New York: Wiley.

    Book  MATH  Google Scholar 

  • Ripley, B. (1996). Pattern recognition and neural networks. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  • Ripley, B. (2004). Selecting amongst large classes of models. In N. Adams, M. Crowder, D. Hand, & D. Stephens (Eds.), Methods and models in statistics: In honor of Professor John Nelder, FRS (pp. 155–170). London: Imperial College Press.

    Chapter  Google Scholar 

  • Robert, C. (2001). The Bayesian choice (2nd ed.). New York: Springer.

    MATH  Google Scholar 

  • Roberts, G., & Sahu, S. (1997). Updating schemes, correlation structure, blocking and parameterization for the Gibbs sampler. Journal of the Royal Statistical Society, Series B59, 291–317.

    Article  MathSciNet  MATH  Google Scholar 

  • Roberts, G., Gelman, A., & Gilks, W. (1997). Weak convergence and optimal scaling of random walk Metropolis algorithms. The Annals of Applied Probability7, 110–120.

    Article  MathSciNet  MATH  Google Scholar 

  • Robinson, G. (1991). That BLUP is a good thing (with discussion). Statistical Science6, 15–51.

    Article  MathSciNet  MATH  Google Scholar 

  • Robinson, L., & Jewell, N. (1991). Some surprising results about covariate adjustment in logistic regression models. International Statistical Review59, 227–240.

    Article  MATH  Google Scholar 

  • Rosenbaum, P. (2002). Observational studies (2nd ed.). New York: Springer.

    MATH  Google Scholar 

  • Rothman, K., & Greenland, S. (1998). Modern epidemiology (2nd ed.). Philadelphia: Lipincott, Williams and Wilkins.

    Google Scholar 

  • Royall, R. (1986). Model robust confidence intervals using maximum likelihood estimators. International Statistical Review54, 221–226.

    Article  MathSciNet  MATH  Google Scholar 

  • Royall, R. (1997). Statistical evidence – a likelihood paradigm. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Rue, H., & Held, L. (2005). Gaussian Markov random fields: Theory and application. Boca Raton: Chapman and Hall/CRC.

    Book  Google Scholar 

  • Rue, H., Martino, S., & Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations (with discussion). Journal of the Royal Statistical Society, Series B71, 319–392.

    Article  MathSciNet  MATH  Google Scholar 

  • Ruppert, D., Wand, M., & Carroll, R. (2003). Semiparametric regression. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Salway, R., & Wakefield, J. (2008). Gamma generalized linear models for pharmacokinetic data. Biometrics64, 620–626.

    Article  MathSciNet  MATH  Google Scholar 

  • Savage, L. (1972). The foundations of statistics (2nd ed.). New York: Dover.

    MATH  Google Scholar 

  • Scheffé, H. (1959). The analysis of variance. New York: Wiley.

    MATH  Google Scholar 

  • Schervish, M. (1995). Theory of statistics. New York: Springer.

    Book  MATH  Google Scholar 

  • Schott, J. (1997). Matrix analysis for statistics. New York: Wiley.

    MATH  Google Scholar 

  • Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics6, 461–464.

    Article  MathSciNet  MATH  Google Scholar 

  • Seaman, S., & Richardson, S. (2004). Equivalence of prospective and retrospective models in the Bayesian analysis of case-control studies. Biometrika91, 15–25.

    Article  MathSciNet  MATH  Google Scholar 

  • Searle, S., Casella, G., & McCulloch, C. (1992). Variance components. New York: Wiley.

    Book  MATH  Google Scholar 

  • Seber, G., & Lee, S. (2003). Linear regression analysis (2nd ed.). New York: Wiley.

    Book  MATH  Google Scholar 

  • Seber, G., & Wild, C. (1989). Nonlinear regression. New York: Wiley.

    Book  MATH  Google Scholar 

  • Sellke, T., Bayarri, M., & Berger, J. (2001). Calibration of p values for testing precise null hypotheses. The American Statistician55, 62–71.

    Article  MathSciNet  MATH  Google Scholar 

  • Sheather, S., & Jones, M. (1991). A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society, Series B53, 683–690.

    MathSciNet  MATH  Google Scholar 

  • Sidák, Z. (1967). Rectangular confidence region for the means of multivariate normal distributions. Journal of the American Statistical Association62, 626–633.

    MathSciNet  MATH  Google Scholar 

  • Silverman, B. (1985). Some aspects of the spline smoothing approach to non-parametric regression curve fitting. Journal of the Royal Statistical Society, Series B47, 1–52.

    MATH  Google Scholar 

  • Simonoff, J. (1997). Smoothing methods in statistics. New York: Springer.

    Google Scholar 

  • Simpson, E. (1951). The interpretation of interaction in contingency tables. Journal of the Royal Statistical Society, Series B13, 238–241.

    MATH  Google Scholar 

  • Singh, K. (1981). On the asymptotic accuracy of Efron’s bootstrap. Annals of Statistics9, 1187–1195.

    Article  MathSciNet  MATH  Google Scholar 

  • Smith, A., & Gelfand, A. (1992). Bayesian statistics without tears: A sampling-resampling perspective. The American Statistician46, 84–88.

    MathSciNet  Google Scholar 

  • Smith, C. (1947). Some examples of discrimination. Annals of Eugenics13, 272–282.

    Google Scholar 

  • Smyth, G., & Verbyla, A. (1996). A conditional likelihood approach to residual maximum likelihood estimation in generalized linear models. Journal of the Royal Statistical Society, Series B58, 565–572.

    MathSciNet  MATH  Google Scholar 

  • Sommer, A. (1982). Nutritional blindness. Oxford: Oxford University Press.

    Google Scholar 

  • Spiegelhalter, D., Best, N., Carlin, B., & van der Linde, A. (1998). Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society, Series B64, 583–639.

    Google Scholar 

  • Stamey, T., Kabalin, J., McNeal, J., Johnstone, I., Freiha, F., Redwine, E., & Yang, N. (1989). Prostate specific antigen in the diagnosis and treatment of adenocarcinoma of the prostate, II Radical prostatectomy treated patients. Journal of Urology141, 1076–1083.

    Google Scholar 

  • Stone, M. (1977). An asymptotic equivalence of choice of model by cross-validation and Akaike’s criterion. Journal of the Royal Statistical Society, Series B39, 44–47.

    MATH  Google Scholar 

  • Storey, J. (2002). A direct approach to false discovery rates. Journal of the Royal Statistical Society, Series B64, 479–498.

    Article  MathSciNet  MATH  Google Scholar 

  • Storey, J. (2003). The positive false discovery rate: A Bayesian interpretation and the q-value. The Annals of Statistics31, 2013–2035.

    Article  MathSciNet  MATH  Google Scholar 

  • Storey, J., Madeoy, J., Strout, J., Wurfel, M., Ronald, J., & Akey, J. (2007). Gene-expression variation within and among human populations. American Journal of Human Genetics80, 502–509.

    Article  Google Scholar 

  • Sun, J., & Loader, C. (1994). Confidence bands for linear regression and smoothing. The Annals of Statistics22, 1328–1345.

    Article  MathSciNet  MATH  Google Scholar 

  • Szpiro, A., Rice, K., & Lumley, T. (2010). Model-robust regression and a Bayesian “sandwich” estimator. Annals of Applied Statistics4, 2099–2113.

    Article  MathSciNet  MATH  Google Scholar 

  • Thall, P., & Vail, S. (1990). Some covariance models for longitudinal count data with overdispersion. Biometrics46, 657–671.

    Article  MathSciNet  MATH  Google Scholar 

  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B58, 267–288.

    MathSciNet  MATH  Google Scholar 

  • Tibshirani, R. (2011). Regression shrinkage and selection via the lasso: a retrospective (with discussion). Journal of the Royal Statistical Society, Series B73, 273–282.

    Article  MathSciNet  Google Scholar 

  • Tierney, L., & Kadane, J. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association81, 82–86.

    Article  MathSciNet  MATH  Google Scholar 

  • Titterington, D., Murray, G., Murray, L., Spiegelhalter, D., Skene, A., Habbema, J., & Gelpke, G. (1981). Comparison of discrimination techniques applied to a complex data set of head injured patients. Journal of the Royal Statistical Society, Series A144, 145–175.

    Article  MathSciNet  MATH  Google Scholar 

  • Upton, R., Thiercelin, J., Guentert, T., Wallace, S., Powell, J., Sansom, L., & Riegelman, S. (1982). Intraindividual variability in Theophylline pharmacokinetics: statistical verification in 39 of 60 healthy young adults. Journal of Pharmacokinetics and Biopharmaceutics10, 123–134.

    Google Scholar 

  • van der Vaart, A. (1998). Asymptotic statistics. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  • Vapnick, V. (1996). The nature of statistical learning theory. New York: Springer.

    Google Scholar 

  • Verbeeke, G., & Molenberghs, G. (2000). Linear mixed models for longitudinal data. New York: Springer.

    Google Scholar 

  • Wabha, G. (1983). Bayesian ‘confidence intervals’ for the cross-validated smoothing spline. Journal of the Royal Statistical Society, Series B45, 133–150.

    Google Scholar 

  • Wabha, G. (1985). A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline problem. Annals of Statistics13, 1378–1402.

    Article  MathSciNet  Google Scholar 

  • Wabha, G. (1990). Spline models for observational data. Philadelphia: SIAM.

    Google Scholar 

  • Wakefield, J. (1996). Bayesian individualization via sampling-based methods. Journal of Pharmacokinetics and Biopharmaceutics24, 103–131.

    Google Scholar 

  • Wakefield, J. (2004). Non-linear regression modelling. In N. Adams, M. Crowder, D. Hand, & D. Stephens (Eds.), Methods and models in statistics: In honor of Professor John Nelder, FRS (pp. 119–153). London: Imperial College Press.

    Chapter  Google Scholar 

  • Wakefield, J. (2007a). A Bayesian measure of the probability of false discovery in genetic epidemiology studies. American Journal of Human Genetics81, 208–227.

    Article  Google Scholar 

  • Wakefield, J. (2007b). Disease mapping and spatial regression with count data. Biostatistics, 8, 158–183.

    Article  MATH  Google Scholar 

  • Wakefield, J. (2008). Ecologic studies revisited. Annual Review of Public Health29, 75–90.

    Article  Google Scholar 

  • Wakefield, J. (2009a). Bayes factors for genome-wide association studies: Comparison with p-values. Genetic Epidemiology33, 79–86.

    Article  Google Scholar 

  • Wakefield, J. (2009b). Multi-level modelling, the ecologic fallacy, and hybrid study designs. International Journal of Epidemiology38, 330–336.

    Article  Google Scholar 

  • Wakefield, J., Smith, A., Racine-Poon, A., & Gelfand, A. (1994). Bayesian analysis of linear and non-linear population models using the Gibbs sampler. Applied Statistics43, 201–221.

    Article  MATH  Google Scholar 

  • Wakefield, J., Aarons, L., & Racine-Poon, A. (1999). The Bayesian approach to population pharmacokinetic/pharmacodynamic modelling. In C. Gatsonis, R. E. Kass, B. P. Carlin, A. L. Carriquiry, A. Gelman, I. Verdinelli, & M. West (Eds.), Case studies in Bayesian statistics, volume IV (pp. 205–265). New York: Springer.

    Chapter  Google Scholar 

  • Wald, A. (1943). Tests of statistical hypotheses concerning several parameters when the number of observations is large. Transactions of the American Mathematical Society54, 426–482.

    Article  MathSciNet  MATH  Google Scholar 

  • Wand, M., & Jones, M. (1995). Kernel smoothing. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Wand, M., & Ormerod, J. (2008). On semiparametric regression with O’Sullivan penalised splines. Australian and New Zealand Journal of Statistics50, 179–198.

    Article  MathSciNet  MATH  Google Scholar 

  • Watson, G. (1964). Smooth regression analysis. SankhyaA26, 359–372.

    Google Scholar 

  • Wedderburn, R. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika61, 439–447.

    MathSciNet  MATH  Google Scholar 

  • Wedderburn, R. (1976). On the existence and uniqueness of the maximum likelihood estimates for certain generalized linear models. Biometrika63, 27–32.

    Article  MathSciNet  MATH  Google Scholar 

  • West, M. (1993). Approximating posterior distributions by mixtures. Journal of the Royal Statistical Society, Series B55, 409–422.

    MATH  Google Scholar 

  • West, M., & Harrison, J. (1997). Bayesian forecasting and dynamic models (2nd ed.). New York: Springer.

    MATH  Google Scholar 

  • Westfall, P., Johnson, W., & Utts, J. (1995). A Bayesian perspective on the Bonferroni adjustment. Biometrika84, 419–427.

    Article  MathSciNet  Google Scholar 

  • White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica48, 1721–746.

    Google Scholar 

  • White, J. (1982). A two stage design for the study of the relationship between a rare exposure and a rare disease. American Journal of Epidemiology115, 119–128.

    Google Scholar 

  • Wood, S. (2006). Generalized additive models: An introduction with R. Boca Raton: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Wood, S. (2008). Fast stable direct fitting and smoothness selection for generalized additive models. Journal of the Royal Statistical Society, Series B70, 495–518.

    Article  MATH  Google Scholar 

  • Wood, S. (2011). Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. Journal of the Royal Statistical Society, Series B, 73, 3–36.

    Article  Google Scholar 

  • Wu, T., & Lange, K. (2008). Coordinate descent algorithms for lasso penalized regression. The Annals of Applied Statistics2, 224–244.

    Article  MathSciNet  MATH  Google Scholar 

  • Yates, F. (1984). Tests of significance for 2 ×2 contingency tables. Journal of the Royal Statistical Society, Series B147, 426–463.

    Article  MathSciNet  MATH  Google Scholar 

  • Yee, T., & Wild, C. (1996). Vector generalized additive models. Journal of the Royal Statistical Society, Series B58, 481–493.

    MathSciNet  MATH  Google Scholar 

  • Yu, K., & Jones, M. (2004). Likelihood-based local linear estimation of the conditional variance function. Journal of the American Statistical Association99, 139–144.

    Article  MathSciNet  MATH  Google Scholar 

  • Yuan, M., & Lin, Y. (2007). Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society, Series B68, 49–67.

    MathSciNet  Google Scholar 

  • Zeger, S., & Liang, K. (1986). Longitudinal data analysis for discrete and continuous outcomes. Biometrics42, 121–130.

    Article  Google Scholar 

  • Zhao, L., & Prentice, R. (1990). Correlated binary regression using a generalized quadratic model. Biometrika77, 642–648.

    Article  MathSciNet  Google Scholar 

  • Zhao, L., Prentice, R., & Self, S. (1992). Multivariate mean parameter estimation by using a partly exponential model. Journal of the Royal Statistical Society, Series B54, 805–811.

    Google Scholar 

  • Zou, H., & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society, Series B67, 301–320.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media New York

About this chapter

Cite this chapter

Wakefield, J. (2012). Some Results from Classical Statistics. In: Bayesian and Frequentist Regression Methods. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0925-1_18

Download citation

Publish with us

Policies and ethics