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M-Estimation (Estimating Equations)

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Part of the book series: Springer Texts in Statistics ((STS,volume 120))

Abstract

In Chapter 1 we made the distinction between the parts of a fully specified statistical model. The primary part is the part that is most important for answering the underlying scientific questions. The secondary part consists of all the remaining details of the model. Usually the primary part is the mean or systematic part of the model, and the secondary part is mainly concerned with the distributional assumptions about the random part of the model. The full specification of the model is important for constructing the likelihood and for using the associated classical methods of inference as spelled out in Chapters 2 and 3 and supported by the asymptotic results of Chapter 6.

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References

  • Agresti, A. (2002).Categorical Data Analysis. New Jersey: Wiley.

    Book  MATH  Google Scholar 

  • Agresti, A. and Coull, B. A. (1998). Approximate is better than “exact” for interval estimation of binomial proportions.The American Statistician, 52:119–126.

    MathSciNet  Google Scholar 

  • Agresti, A. and Min, Y. (2005). Frequentist performance of Bayesian confidence intervals for comparing proportions in 2 ×2 contingency tables.Biometrics, 61(2):515–523.

    Article  MATH  MathSciNet  Google Scholar 

  • Aitchison, J. and Silvey, S. D. (1958). Maximum-likelihood estimation of parameters subject to restraints.The Annals of Mathematical Statistics, 29:813–828.

    Article  MATH  MathSciNet  Google Scholar 

  • Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Petrov, B. N. e. and Czaki, F. e., editors,2nd International Symposium on Information Theory, pages 267–281. Akademiai Kiado.

    Google Scholar 

  • Akritas, M. G. (1990). The rank transform method in some two-factor designs.Journal of the American Statistical Association, 85:73–78.

    Article  MATH  MathSciNet  Google Scholar 

  • Akritas, M. G. (1991). Limitations of the rank transform procedure: A study of repeated measures designs. Part I.Journal of the American Statistical Association, 86:457–460.

    Google Scholar 

  • Anderson, M. J. and Robinson, J. (2001). Permutation tests for linear models.Australian & New Zealand Journal of Statistics, 43(1):75–88.

    Article  MATH  MathSciNet  Google Scholar 

  • Andrews, D. W. K. (1987). Asymptotic results for generalized Wald tests.Econometric Theory, 3:348–358.

    Article  Google Scholar 

  • Arvesen, J. N. (1969). Jackknifing u-statistics.The Annals of Mathematical Statistics, 40:2076–2100.

    Article  MATH  MathSciNet  Google Scholar 

  • Bahadur, R. R. (1964). On Fisher’s bound for asymptotic variances.The Annals of Mathematical Statistics, 35:1545–1552.

    Article  MATH  MathSciNet  Google Scholar 

  • Bahadur, R. R. (1966). A note on quantiles in large samples.The Annals of Mathematical Statistics, 37:577–580.

    Article  MATH  MathSciNet  Google Scholar 

  • Barlow, R. E., Bartholomew, D. J., B. J. M., and Brunk, H. D. (1972).Statistical Inference under order restrictions: the theory and application of isotonic regression. John Wiley & Sons.

    Google Scholar 

  • Barnard, G. A. (1945). A new test for 2 × 2 tables.Nature, 156:177.

    Article  MATH  MathSciNet  Google Scholar 

  • Barnard, G. A. (1947). Significance tests for 2 × 2 tables.Biometrika, 34:123–138.

    MATH  MathSciNet  Google Scholar 

  • Barnard, G. A. (1963). Discussion on “the spectral analysis of point processes”.Journal of the Royal Statistical Society, Series B: Statistical Methodology, 25:294–294.

    MathSciNet  Google Scholar 

  • Barndorff-Nielsen, O. (1978).Information and Exponential Families in Statistical Theory. John Wiley & Sons.

    Google Scholar 

  • Barndorff-Nielsen, O. (1982). Exponential families. In Banks, D. L., Read, C. B., and Kotz, S., editors,Encyclopedia of Statistical Sciences (9 vols. plus Supplement), Volume 2, pages 587–596. John Wiley & Sons.

    Google Scholar 

  • Barndorff-Nielsen, O. and Cox, D. R. (1979). Edgeworth and saddle-point approximations with statistical applications (C/R p299-312).Journal of the Royal Statistical Society, Series B: Methodological, 41:279–299.

    MATH  MathSciNet  Google Scholar 

  • Bartholomew, D. J. (1957). A problem in life testing.Journal of the American Statistical Association, 52:350–355.

    Article  Google Scholar 

  • Bartholomew, D. J. (1959). A test of homogeneity for ordered alternatives.Biometrika, 46:36–48.

    Article  MATH  MathSciNet  Google Scholar 

  • Benichou, J. and Gail, M. H. (1989). A delta method for implicitly defined random variables (C/R: 90V44 p58).The American Statistician, 43:41–44.

    MathSciNet  Google Scholar 

  • Beran, R. (1986). Simulated power functions.The Annals of Statistics, 14:151–173.

    Article  MATH  MathSciNet  Google Scholar 

  • Beran, R. (1988). Prepivoting test statistics: A bootstrap view of asymptotic refinements.Journal of the American Statistical Association, 83:687–697.

    Article  MATH  MathSciNet  Google Scholar 

  • Beran, R. and Srivastava, M. S. (1985). Bootstrap tests and confidence regions for functions of a covariance matrix (Corr: V15 p470-471).The Annals of Statistics, 13:95–115.

    Article  MATH  MathSciNet  Google Scholar 

  • Berger, J. O. and Wolpert, R. L. (1984).The Likelihood Principle. Institute of Mathematical Statistics.

    Google Scholar 

  • Berger, R. L. (1996). More powerful tests from confidence intervalp values.The American Statistician, 50:314–318.

    Google Scholar 

  • Berger, R. L. and Boos, D. D. (1994).P values maximized over a confidence set for the nuisance parameter.Journal of the American Statistical Association, 89:1012–1016.

    MATH  MathSciNet  Google Scholar 

  • Berndt, E. R. and Savin, N. E. (1977). Conflict among criteria for testing hypotheses in the multivariate linear regression model.Econometrica, 45:1263–1277.

    Article  MATH  MathSciNet  Google Scholar 

  • Best, D. J. and Rayner, J. C. W. (1987). Welch’s approximate solution for the Behrens-Fisher problem.Technometrics, 29:205–210.

    MATH  MathSciNet  Google Scholar 

  • Bhattacharyya, G. K. and Johnson, R. A. (1973). On a test of independence in a bivariate exponential distribution.Journal of the American Statistical Association, 68:704–706.

    Article  MATH  MathSciNet  Google Scholar 

  • Bickel, P. J. (1974). Edgeworth expansions in nonparametric statistics.The Annals of Statistics, 2:1–20.

    Article  MATH  MathSciNet  Google Scholar 

  • Bickel, P. J. and Doksum, K. A. (1981). An analysis of transformations revisited.Journal of the American Statistical Association, 76:296–311.

    Article  MATH  MathSciNet  Google Scholar 

  • Bickel, P. J. and Freedman, D. A. (1981). Some asymptotic theory for the bootstrap.The Annals of Statistics, 9:1196–1217.

    Article  MATH  MathSciNet  Google Scholar 

  • Bickel, P. J. and van Zwet, W. R. (1978). Asymptotic expansions for the power of distribution free tests in the two-sample problem (Corr: V6 p1170-1171).The Annals of Statistics, 6:937–1004.

    Article  MATH  MathSciNet  Google Scholar 

  • Billingsley, P. (1999).Convergence of Probability Measures. John Wiley & Sons.

    Google Scholar 

  • Birmbaum, L. S., Morrissey, R. E., and Harris, M. W. (1991). Teratogenic effects of 2,3,7,8-tetrabromodibenzo-p-dioxin and three polybrominated dibenzofurans in c57bl/6n mice.Toxicology and Applied Pharmacology, 107:141–152.

    Article  Google Scholar 

  • Boos, D., Janssen, P., and Veraverbeke, N. (1989). Resampling from centered data in the two-sample problem.Journal of Statistical Planning and Inference, 21:327–345.

    Article  MATH  MathSciNet  Google Scholar 

  • Boos, D. D. (1992). On generalized score tests (Com: 93V47 p311-312).The American Statistician, 46:327–333.

    Google Scholar 

  • Boos, D. D. (2003). Introduction to the bootstrap world.Statistical Science, 18(2):168–174.

    Article  MathSciNet  Google Scholar 

  • Boos, D. D. and Brownie, C. (1992). A rank-based mixed model approach to multisite clinical trials (Corr: 94V50 p322).Biometrics, 48:61–72.

    Article  Google Scholar 

  • Boos, D. D. and Brownie, C. (2004). Comparing variances and other measures of dispersion.Statistical Science, 19(4):571–578.

    Article  MATH  MathSciNet  Google Scholar 

  • Boos, D. D. and Hughes-Oliver, J. M. (2000). How large doesn have to be forZ andt intervals?The American Statistician, 54(2):121–128.

    Google Scholar 

  • Boos, D. D. and Monahan, J. F. (1986). Bootstrap methods using prior information.Biometrika, 73:77–83.

    Article  Google Scholar 

  • Boos, D. D. and Zhang, J. (2000). Monte Carlo evaluation of resampling-based hypothesis tests.Journal of the American Statistical Association, 95(450):486–492.

    Article  Google Scholar 

  • Booth, J. and Presnell, B. (1998). Allocation of Monte Carlo resources for the iterated bootstrap.Journal of Computational and Graphical Statistics, 7:92–112.

    MathSciNet  Google Scholar 

  • Booth, J. G. and Hall, P. (1994). Monte Carlo approximation and the iterated bootstrap.Biometrika, 81:331–340.

    MATH  MathSciNet  Google Scholar 

  • Boschloo, R. D. (1970). Raised conditional level of significance for the 2 × 2-table when testing the equality of two probabiities.Statistica Neerlandica, 24:1–35.

    Article  MATH  MathSciNet  Google Scholar 

  • Box, G. E. P. and Andersen, S. L. (1955). Permutation theory in the derivation of robust criteria and the study of departures from assumption.Journal of the Royal Statistical Society, Series B: Statistical Methodology, 17:1–16.

    MATH  Google Scholar 

  • Box, G. E. P. and Cox, D. R. (1964). An analysis of transformations.Journal of the Royal Statistical Society Series B-Statistical Methodology, 26:211–252.

    MATH  MathSciNet  Google Scholar 

  • Box, G. E. P. and Watson, G. S. (1962). Robustness to non-normality of regression tests (Corr: V52 p669).Biometrika, 49:93–106.

    Article  MATH  MathSciNet  Google Scholar 

  • Breslow, N. (1989). Score tests in overdispersed GLM’s. In Decarli, A., Francis, B. J., Gilchrist, R., and Seeber, G. U. H., editors,Statistical Modelling, pages 64–74. Springer-Verlag Inc.

    Google Scholar 

  • Breslow, N. (1990). Tests of hypotheses in overdispersed Poisson regression and other quasi-likelihood models.Journal of the American Statistical Association, 85:565–571.

    Article  Google Scholar 

  • Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models.Journal of the American Statistical Association, 88:9–25.

    MATH  Google Scholar 

  • Brockwell, S. E. and Gordon, I. R. (2007). A simple method for inference on an overall effect in meta-analysis.Statistics in Medicine, 26(25):4531–4543.

    Article  MathSciNet  Google Scholar 

  • Brown, L., Cai, T., DasGupta, A., Agresti, A., Coull, B., Casella, G., Corcoran, C., Mehta, C., Ghosh, M., Santner, T., Brown, L., Cai, T., and DasGupta, A. (2001). Interval estimation for a binomial proportion - comment - rejoinder.Statistical Science, 16(2):101–133.

    MATH  MathSciNet  Google Scholar 

  • Brown, L. D. (1986).Fundamentals of Statistical Exponential Families: with Applications in Statistical Decision Theory. Institute of Mathematical Statistics.

    Google Scholar 

  • Brownie, C., Anderson, D. R., Burnham, K. P., and Robson, D. S. (1985).Statistical Inference from Band Recovery Data: A Handbook (Second Edition). U.S. Fish and Wildlife Service [U.S. Department of Interior].

    Google Scholar 

  • Brownie, C. and Boos, D. D. (1994). Type I error robustness of ANOVA and ANOVA on ranks when the number of treatments is large.Biometrics, 50:542–549.

    Article  MATH  Google Scholar 

  • Brownie, C. F. and Brownie, C. (1986). Teratogenic effect of calcium edetate (caedta) in rats and the protective effect of zinc).Toxicology and Applied Pharmacology, 82(3):426–443.

    Article  MathSciNet  Google Scholar 

  • Carlstein, E. (1986). The use of subseries values for estimating the variance of a general statistic from a stationary sequence.The Annals of Statistics, 14:1171–1179.

    Article  MATH  MathSciNet  Google Scholar 

  • Carroll, R. J. and Ruppert, D. (1984). Power transformations when fitting theoretical models to data.Journal of the American Statistical Association, 79:321–328.

    Article  MathSciNet  Google Scholar 

  • Carroll, R. J. and Ruppert, D. (1988).Transformation and weighting in regression. Chapman & Hall Ltd.

    Google Scholar 

  • Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006).Measurement error in nonlinear models: a modern perspective. Chapman & Hall.

    Google Scholar 

  • Casella, G. and Berger, R. L. (2002).Statistical Inference. Duxbury Press.

    Google Scholar 

  • Chernoff, H. (1954). On the distribution of the likelihood ratio.Annals of Mathematical Statistics, 25(3):573–578.

    Article  MATH  MathSciNet  Google Scholar 

  • Chernoff, H. and Lehmann, E. L. (1954). The use of maximum likelihood estimates in χ2 tests for goodness of fit.Annals of Mathematical Statistics, 25:579–586.

    Article  MATH  MathSciNet  Google Scholar 

  • Coles, S. G. and Dixon, M. J. (1999). Likelihood-based inference for extreme value models.Extremes, 2:5–23.

    Article  MATH  Google Scholar 

  • Conover, W. J. (1973). Rank tests for one sample, two samples, andk samples without the assumption of a continuous distribution function.The Annals of Statistics, 1:1105–1125.

    Article  MATH  MathSciNet  Google Scholar 

  • Conover, W. J. and Iman, R. L. (1981). Rank transformations as a bridge between parametric and nonparametric statistics (C/R: P129-133).The American Statistician, 35:124–129.

    MATH  Google Scholar 

  • Conover, W. J. and Salsburg, D. S. (1988). Locally most powerful tests for detecting treatment effects when only a subset of patients can be expected to “respond” to treatment.Biometrics, 44:189–196.

    Article  MATH  MathSciNet  Google Scholar 

  • Cook, J. R. and Stefanski, L. A. (1994). Simulation-extrapolation estimation in parametric measurement error models.Journal of the American Statistical Association, 89:1314–1328.

    Article  MATH  Google Scholar 

  • Cook, S. R., Gelman, A., and Rubin, D. B. (2006). Validation of software for Bayesian models using posterior quantiles.Journal of Computational and Graphical Statistics, 15(3):675–692.

    Article  MathSciNet  Google Scholar 

  • Cox, D. R. (1970).Analysis of binary Data. Chapman & Hall.

    Google Scholar 

  • Cox, D. R. and Snell, E. J. (1981).Applied statistics: principles and examples. Chapman & Hall Ltd.

    Google Scholar 

  • Cox, D. R. and Snell, E. J. (1989).Analysis of Binary Data. Chapman & Hall Ltd.

    Google Scholar 

  • Cramér, H. (1946).Mathematical Methods of Statistics. Princeton University Press.

    Google Scholar 

  • Cressie, N. and Read, T. R. C. (1984). Multinomial goodness-of-fit tests.Journal of the Royal Statistical Society, Series B: Methodological, 46:440–464.

    MATH  MathSciNet  Google Scholar 

  • Dacunha-Castelle, D. and Gassiat, E. (1999). Testing the order of a model using locally conic parametrization: Population mixtures and stationary ARMA processes.The Annals of Statistics, 27(4):1178–1209.

    Article  MATH  MathSciNet  Google Scholar 

  • Darmois, G. (1935). The laws of probability to exhaustive estimation.Comptes rendus hebdomadaires des seances de l academie des sciences, 200:1265–1266.

    Google Scholar 

  • David, H. A. (1998). First (?) occurrence of common terms in probability and statistics — A second list, with corrections (Corr: 1998V52 p371).The American Statistician, 52:36–40.

    MathSciNet  Google Scholar 

  • Davies, R. B. (1977). Hypothesis testing when a nuisance parameter is present only under the alternative.Biometrika, 64:247–254.

    Article  MATH  MathSciNet  Google Scholar 

  • Davies, R. B. (1987). Hypothesis testing when a nuisance parameter is present only under the alternative.Biometrika, 74:33–43.

    MATH  MathSciNet  Google Scholar 

  • Davison, A. C. and Hinkley, D. V. (1997).Bootstrap Methods and Their Application. Cambridge University Press.

    Google Scholar 

  • DeGroot, M. H. (1970).Optimal Statistical Decisions. New York, McGraw-Hill.

    MATH  Google Scholar 

  • Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood from incomplete data via em algorithm.Journal of the Royal Statistical Society Series B-Methodological, 39:1–38.

    MATH  MathSciNet  Google Scholar 

  • DerSimonian, R. and Laird, N. (1986). Meta-analysis in clinical trials.Controlled Clinical Trials, 7:177–188.

    Article  Google Scholar 

  • DiCiccio, T. and Tibshirani, R. (1987). Bootstrap confidence intervals and bootstrap approximations.Journal of the American Statistical Association, 82:163–170.

    Article  MATH  MathSciNet  Google Scholar 

  • DiCiccio, T. J. and Efron, B. (1996). Bootstrap confidence intervals (Disc: P212-228).Statistical Science, 11:189–212.

    Article  MATH  MathSciNet  Google Scholar 

  • Diggle, P. J., Heagerty, P., Liang, K.-Y., and Zeger, S. L. (2002).Analysis of Longitudinal Data. Oxford University Press.

    Google Scholar 

  • Doksum, K. and Bickel, P. (1969). Test for monotone failure rate based on normalized spacing.The Annals of Mathematical Statistics, 40:1216–1235.

    Article  MATH  MathSciNet  Google Scholar 

  • Donald, A. and Donner, A. (1990). A simulation study of the analysis of sets of 2 ×2 contingency tables under cluster sampling: Estimation of a common odds ratio.Journal of the American Statistical Association, 85:537–543.

    Google Scholar 

  • Dubey, S. D. (1967). Some percentile estimators for Weibull parameters.Technometrics, 9:119–129.

    Article  MathSciNet  Google Scholar 

  • Dubinin, T. M. and Vardeman, S. B. (2003). Likelihood-based inference in some continuous exponential families with unknown threshold parameters.Journal of the American Statistical Association, 98(463):741–749.

    Article  MATH  MathSciNet  Google Scholar 

  • Dunlop, D. D. (1994). Regression for longitudinal data: A bridge from least squares regression.The American Statistician, 48:299–303.

    MathSciNet  Google Scholar 

  • Efron, B. (1979). Bootstrap methods: Another look at the jackknife.The Annals of Statistics, 7:1–26.

    Article  MATH  MathSciNet  Google Scholar 

  • Efron, B. (1982).The Jackknife, the Bootstrap and Other Resampling Plans. SIAM [Society for Industrial and Applied Mathematics].

    Google Scholar 

  • Efron, B. (1987). Better bootstrap confidence intervals (C/R: P186-200).Journal of the American Statistical Association, 82:171–185.

    Article  MATH  MathSciNet  Google Scholar 

  • Efron, B. and Hinkley, D. V. (1978). Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information (C/R: P482-487).Biometrika, 65:457–481.

    Article  MATH  MathSciNet  Google Scholar 

  • Efron, B. and Morris, C. (1972). Empirical Bayes on vector observations: An extension of Stein’s method.Biometrika, 59:335–347.

    Article  MATH  MathSciNet  Google Scholar 

  • Efron, B. and Morris, C. (1973). Stein’s estimation rule and its competitors – An empirical Bayes approach.Journal of the American Statistical Association, 68:117–130.

    MATH  MathSciNet  Google Scholar 

  • Efron, B. and Stein, C. (1981). The jackknife estimate of variance.The Annals of Statistics, 9:586–596.

    Article  MATH  MathSciNet  Google Scholar 

  • Efron, B. and Tibshirani, R. (1993).An Introduction to the Bootstrap. Chapman & Hall Ltd.

    Google Scholar 

  • Ehrenberg, A. S. C. (1977). Rudiments of numeracy (Pkg: P277-323).Journal of the Royal Statistical Society, Series A: General, 140:277–297.

    Article  Google Scholar 

  • Ehrenberg, A. S. C. (1978).Data Reduction: Analysing and Interpreting Statistical Data (Revised Reprint). John Wiley & Sons.

    Google Scholar 

  • Ehrenberg, A. S. C. (1981). The problem of numeracy.The American Statistician, 35:67–71.

    Google Scholar 

  • El-Shaarawi, A. H. (1985). Some goodness-of-fit methods for the Poisson plus added zeros distribution.Applied and environmental microbiology, 49:1304–1306.

    Google Scholar 

  • Embrechts, P. A. L., Pugh, D., and Smith, R. L. (1985).Statistical Extremes and Risks. Course Notes. Imperial College, London, Dept. of Mathematics.

    Google Scholar 

  • Fawcett, R. F. and Salter, K. C. (1984). A Monte Carlo study of theF test and three tests based on ranks of treatment effects in randomized block designs.Communications in Statistics: Simulation and Computation, 13:213–225.

    Article  Google Scholar 

  • Fay, M. P. and Graubard, B. I. (2001). Small-sample adjustments for Wald-type tests using sandwich estimators.Biometrics, 57(4):1198–1206.

    Article  MATH  MathSciNet  Google Scholar 

  • Feller, W. (1966).An Introduction to Probability Theory and Its Applications, Vol. II. John Wiley & Sons.

    Google Scholar 

  • Fisher, R. A. (1912). On an absolute criterion for fitting frequency curves.Messenger of Mathematics, 41:155–160.

    Google Scholar 

  • Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics.Philos. Trans. Roy. Soc. London Ser. A, 222:309–368.

    Article  MATH  Google Scholar 

  • Fisher, R. A. (1934a).Statistical Methods for Research Workers, fifth edition. Oliver & Boyd.

    Google Scholar 

  • Fisher, R. A. (1934b). Two new properties of mathematical likelihood.Proceedings of the Royal Society of London. Series A, 144:285–307.

    Article  Google Scholar 

  • Fisher, R. A. (1935).The Design of Experiments (eighth edition, 1966). Hafner Press.

    Google Scholar 

  • Fix, E. and Hodges, J. L. (1955). Significance probabilities of the wilcoxon test.The Annals of Mathematical Statistics, 26:301–312.

    Article  MATH  MathSciNet  Google Scholar 

  • Fouskakis, D. and Draper, D. (2002). Stochastic optimization: A review.International Statistical Review, 70(3):315–349.

    Article  MATH  Google Scholar 

  • Freidlin, B. and Gastwirth, J. L. (2000). Should the median test be retired from general use?The American Statistician, 54(3):161–164.

    Google Scholar 

  • Friedman, M. (1937). The use of ranks to avoid the assumption of normality implicit in the analysis of variance.Journal of the American Statistical Association, 32:675–701.

    Article  Google Scholar 

  • Fuller, W. A. (1987).Measurement Error Models. John Wiley & Sons.

    Google Scholar 

  • Gallant, A. R. (1987).Nonlinear Statistical Models. John Wiley & Sons.

    Google Scholar 

  • Gelfand, A. E. and Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities.Journal of the American Statistical Association, 85:398–409.

    Article  MATH  MathSciNet  Google Scholar 

  • Gelman, A., Pasarica, C., and Dodhia, R. (2002). Let’s practice what we preach: Turning tables into graphs.The American Statistician, 56(2):121–130.

    Article  MathSciNet  Google Scholar 

  • Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images.IEEE Transactions on Pattern Analysis and Machine Intelligence, 6:721–741.

    Article  MATH  Google Scholar 

  • Ghosh, J. K. (1971). A new proof of the Bahadur representation of quantiles and an application.The Annals of Mathematical Statistics, 42:1957–1961.

    Article  MATH  Google Scholar 

  • Glasser, M. (1965). Regression analysis with dependent variable censored.Biometrics, 21:300–306.

    Article  MathSciNet  Google Scholar 

  • Gnedenko, B. V. (1943). Sur la distribution limite du terme maximum d’une série aléatoire.Annals of Mathematics, 44:423–453.

    Article  MATH  MathSciNet  Google Scholar 

  • Godambe, V. P. (1960). An optimum property of regular maximum likelihood estimation (Ack: V32 p1343).The Annals of Mathematical Statistics, 31:1208–1212.

    Article  MathSciNet  Google Scholar 

  • Goffinet, B., Loisel, P., and Laurent, B. (1992). Testing in normal mixture models when the proportions are known.Biometrika, 79:842–846.

    Article  MATH  MathSciNet  Google Scholar 

  • Graybill, F. A. (1976).Theory and Application of the Linear Model. Duxbury Press.

    Google Scholar 

  • Graybill, F. A. (1988).Matrices with Applications in Statistics. Wadsworth.

    Google Scholar 

  • Guilbaud, O. (1979). Interval estimation of the median of a general distribution.Scandinavian Journal of Statistics, 46:29–36.

    MathSciNet  Google Scholar 

  • Haberman, S. J. (1989). Concavity and estimation.The Annals of Statistics, 17:1631–1661.

    Article  MATH  MathSciNet  Google Scholar 

  • Hadi, A. S. and Wells, M. T. (1990). A note on generalized Wald’s method.Metrika, 37:309–315.

    Article  MATH  MathSciNet  Google Scholar 

  • Hajek, J. and Sidak, Z. (1967).Theory of Rank Tests. Academic Press.

    Google Scholar 

  • Hald, A. (1998).A History of Mathematical Statistics from 1750 to 1930. Wiley, New York.

    MATH  Google Scholar 

  • Hall, P. (1986). On the bootstrap and confidence intervals.The Annals of Statistics, 14:1431–1452.

    Article  MATH  MathSciNet  Google Scholar 

  • Hall, P. (1987). Edgeworth expansion for Student’st statistic under minimal moment conditions.The Annals of Probability, 15:920–931.

    Article  MATH  MathSciNet  Google Scholar 

  • Hall, P. (1988). Theoretical comparison of bootstrap confidence intervals (C/R: P953-985).The Annals of Statistics, 16:927–953.

    Article  MATH  MathSciNet  Google Scholar 

  • Hall, P. (1992).The Bootstrap and Edgeworth Expansion. Springer-Verlag Inc.

    Google Scholar 

  • Hall, P. and Titterington, D. M. (1989). The effect of simulation order on level accuracy and power of Monte Carlo tests.Journal of the Royal Statistical Society, Series B: Methodological, 51:459–467.

    MATH  MathSciNet  Google Scholar 

  • Hampel, F. R. (1974). The influence curve and its role in robust estimation.Journal of the American Statistical Association, 69:383–393.

    Article  MATH  MathSciNet  Google Scholar 

  • Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators.Econometrica, 50:1029–1054.

    Article  MATH  MathSciNet  Google Scholar 

  • Harville, D. (1976). Extension of the Gauss-Markov theorem to include the estimation of random effects.The Annals of Statistics, 4:384–395.

    Article  MATH  MathSciNet  Google Scholar 

  • Harville, D. A. (1977). Maximum likelihood approaches to variance component estimation and to related problems (C/R: P338-340).Journal of the American Statistical Association, 72:320–338.

    Article  MATH  MathSciNet  Google Scholar 

  • Hastie, T., Tibshirani, R., and Friedman, J. H. (2001).The Elements of Statistical Learning: Data Mining, Inference, and Prediction: with 200 Full-color Illustrations. Springer-Verlag Inc.

    Google Scholar 

  • Hauck, W. W. and Donner, A. (1977). Wald’s test as applied to hypotheses in logit analysis (Corr: V75 p482).Journal of the American Statistical Association, 72:851–853.

    MATH  MathSciNet  Google Scholar 

  • Heagerty, P. J. and Lumley, T. (2000). Window subsampling of estimating functions with application to regression models.Journal of the American Statistical Association, 95(449):197–211.

    Article  MATH  MathSciNet  Google Scholar 

  • Hernandez, F. and Johnson, R. A. (1980). The large-sample behavior of transformations to normality.Journal of the American Statistical Association, 75:855–861.

    Article  MATH  MathSciNet  Google Scholar 

  • Hettmansperger, T. P. (1984).Statistical Inference Based on Ranks. John Wiley & Sons.

    Google Scholar 

  • Hettmansperger, T. P. and Sheather, S. J. (1986). Confidence intervals based on interpolated order statistics (Corr: V4 p217).Statistics & Probability Letters, 4:75–79.

    Article  MATH  MathSciNet  Google Scholar 

  • Higgins, J. P. T., Thompson, S. G., and Spiegelhalter, D. J. (2009). A re-evaluation of random-effects meta-analysis.Journal of the Royal Statistical Society, Series A: Statistics in Society, 172(1):137–159.

    Article  MathSciNet  Google Scholar 

  • Hinkley, D. V. (1977). Jackknifing in unbalanced situations.Technometrics, 19:285–292.

    Article  MATH  MathSciNet  Google Scholar 

  • Hinkley, D. V. and Runger, G. (1984). The analysis of transformed data (C/R: P309-320).Journal of the American Statistical Association, 79:302–309.

    Article  MATH  MathSciNet  Google Scholar 

  • Hirji, K. F., Mehta, C. R., and Patel, N. R. (1987). Computing distributions for exact logistic regression.Journal of the American Statistical Association, 82:1110–1117.

    Article  MATH  MathSciNet  Google Scholar 

  • Hobert, J. P. and Casella, G. (1996). The effect of improper priors on Gibbs sampling in hierarchical linear mixed models.Journal of the American Statistical Association, 91:1461–1473.

    Article  MATH  MathSciNet  Google Scholar 

  • Hodges, J. L., J. and Lehmann, E. L. (1962). Rank methods for combination of independent experiments in the analysis of variance.The Annals of Mathematical Statistics, 33:482–497.

    Google Scholar 

  • Hodges, J. L. and Lehmann, E. L. (1956). The efficiency of some nonparametric competitors of thet-test.The Annals of Mathematical Statistics, 27:324–335.

    Article  MATH  MathSciNet  Google Scholar 

  • Hodges, J. L. and Lehmann, E. L. (1963). Estimates of location based on rank tests (Ref: V42 p1450-1451).The Annals of Mathematical Statistics, 34:598–611.

    Article  MATH  MathSciNet  Google Scholar 

  • Hoeffding, W. (1948). A class of statistics with asymptotically normal distribution.The Annals of Mathematical Statistics, 19:293–325.

    Article  MATH  MathSciNet  Google Scholar 

  • Hoeffding, W. (1951). A combinatorial central limit theorem.The Annals of Mathematical Statistics, 22:558–566.

    Article  MATH  MathSciNet  Google Scholar 

  • Hoeffding, W. (1952). The large-sample power of tests based on permutations of observations.The Annals of Mathematical Statistics, 23:169–192.

    Article  MATH  MathSciNet  Google Scholar 

  • Hoerl, A. E. and Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems.Technometrics, 12:55–67.

    Article  MATH  Google Scholar 

  • Hope, A. C. A. (1968). A simplified Monte Carlo significance test procedure.Journal of the Royal Statistical Society, Series B: Methodological, 30:582–598.

    MATH  Google Scholar 

  • Hora, S. C. and Iman, R. L. (1988). Asymptotic relative efficiencies of the rank-transformation procedure in randomized complete block designs.Journal of the American Statistical Association, 83:462–470.

    Article  MATH  MathSciNet  Google Scholar 

  • Hosking, J. R. M. (1990).L-moments: Analysis and estimation of distributions using linear combinations of order statistics.Journal of the Royal Statistical Society, Series B: Methodological, 52:105–124.

    MATH  MathSciNet  Google Scholar 

  • Huber, P. J. (1964). Robust estimation of a location parameter.The Annals of Mathematical Statistics, 35:73–101.

    Article  MATH  Google Scholar 

  • Huber, P. J. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. In Neyman, J., editor,Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1, pages 221–233. University of California Press.

    Google Scholar 

  • Huber, P. J. (1973). Robust regression: Asymptotics, conjectures and Monte Carlo.The Annals of Statistics, 1:799–821.

    Article  MATH  MathSciNet  Google Scholar 

  • Huber, P. J. (1981).Robust Statistics. John Wiley & Sons.

    Google Scholar 

  • Hyndman, R. J. and Fan, Y. (1996). Sample quantiles in statistical packages.The American Statistician, 50:361–365.

    Google Scholar 

  • Iverson, H. K. and Randles, R. H. (1989). The effects on convergence of substituting parameter estimates intoU-statistics and other families of statistics.Probability Theory and Related Fields, 81:453–471.

    Article  MATH  MathSciNet  Google Scholar 

  • James, W. and Stein, C. (1961). Estimation with quadratic loss. In Neyman, J., editor,Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1, pages 361–379. University of California Press.

    Google Scholar 

  • Jeffreys, H. (1961).Theory of Probability. Oxford University Press.

    Google Scholar 

  • Jöckel, K.-H. and Jockel, K.-H. (1986). Finite sample properties and asymptotic efficiency of Monte Carlo tests.The Annals of Statistics, 14:336–347.

    Article  MATH  MathSciNet  Google Scholar 

  • Johansen, S. (1979).Introduction to the Theory of Regular Exponential Families. University of Copenhagen.

    Google Scholar 

  • Johnson, R. A., Verrill, S., and Moore, D. H., I. (1987). Two-sample rank tests for detecting changes that occur in a small proportion of the treated population.Biometrics, 43:641–655.

    Google Scholar 

  • Jones, G. L. and Hobert, J. P. (2004). Sufficient burn-in for Gibbs samplers for a hierarchical random effects model.The Annals of Statistics, 32(2):784–817.

    Article  MATH  MathSciNet  Google Scholar 

  • Kackar, R. N. and Harville, D. A. (1984). Approximations for standard errors of estimators of fixed and random effects in mixed linear models.Journal of the American Statistical Association, 79:853–862.

    MATH  MathSciNet  Google Scholar 

  • Kass, R. E. and Steffey, D. (1989). Approximate Bayesian inference in conditionally independent hierarchical models (parametric empirical Bayes models).Journal of the American Statistical Association, 84:717–726.

    Article  MathSciNet  Google Scholar 

  • Kass, R. E. and Wasserman, L. (1996). The selection of prior distributions by formal rules (Corr: 1998V93 p412).Journal of the American Statistical Association, 91:1343–1370.

    Article  MATH  Google Scholar 

  • Kent, J. T. (1982). Robust properties of likelihood ratio tests (Corr: V69 p492).Biometrika, 69:19–27.

    MATH  MathSciNet  Google Scholar 

  • Kenward, M. G. and Roger, J. H. (1997). Small sample inference for fixed effects from restricted maximum likelihood.Biometrics, 53:983–997.

    Article  MATH  Google Scholar 

  • Kepner, J. L. and Wackerly, D. D. (1996). On rank transformation techniques for balanced incomplete repeated-measures designs.Journal of the American Statistical Association, 91:1619–1625.

    MATH  MathSciNet  Google Scholar 

  • Khatri, C. G. (1963). Some results for the singular normal multivariate regression models.Sankhyā, Series A, 30:267–280.

    MathSciNet  Google Scholar 

  • Kilgore, D. L. (1970). The effects of northward dispersal on growth rate of young at birth and litter size in sigmodon hispidus.American Midland Naturalist, 84:510–520.

    Article  Google Scholar 

  • Kim, H.-J. and Boos, D. D. (2004). Variance estimation in spatial regression using a non-parametric semivariogram based on residuals.Scandinavian Journal of Statistics, 31(3):387–401.

    Article  MATH  MathSciNet  Google Scholar 

  • Kim, Y. and Singh, K. (1998). Sharpening estimators using resampling.Journal of Statistical Planning and Inference, 66:121–146.

    Article  MATH  MathSciNet  Google Scholar 

  • Klotz, J. (1962). Non-parametric tests for scale.The Annals of Mathematical Statistics, 33:498–512.

    Article  MATH  MathSciNet  Google Scholar 

  • Koopman, B. O. (1936). On distributions admitting a sufficient statistic.Transactions of the American Mathematical Society, 39(3):399–409.

    Article  MathSciNet  Google Scholar 

  • Kruskal, W. H. and Wallis, W. A. (1952). Use of ranks in one-criterion variance analysis.Journal of the American Statistical Association, 47:583–621.

    Article  MATH  Google Scholar 

  • Künsch, H. R. (1989). The jackknife and the bootstrap for general stationary observations.The Annals of Statistics, 17:1217–1241.

    Article  MATH  MathSciNet  Google Scholar 

  • Laird, N. M. and Ware, J. H. (1982). Random-effects models for longitudinal data.Biometrics, 38:963–974.

    Article  MATH  Google Scholar 

  • Lambert, D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing.Technometrics, 34:1–14.

    Article  MATH  Google Scholar 

  • Landis, J. R., Heyman, E. R., and Koch, G. G. (1978). Average partial association in three-way contingency tables: A review and and discussion of alternative tests.International Statistical Review, 46:237–254.

    Article  MATH  MathSciNet  Google Scholar 

  • Larsen, R. J. and Marx, M. L. (2001).An Introduction to Mathematical Statistics and Its Applications. Prentice-Hall Inc.

    Google Scholar 

  • Lawless, J. F. (1982).Statistical Models and Methods for Lifetime Data. John Wiley & Sons.

    Google Scholar 

  • Lawley, D. N. (1956). A general method for approximating to the distribution of likelihood ratio criteria.Biometrika, 43:295–303.

    Article  MATH  MathSciNet  Google Scholar 

  • Leadbetter, M. R., Lindgren, G., and Rootzén, H. (1983).Extremes and Related Properties of Random Sequences and Processes. Springer-Verlag Inc.

    Google Scholar 

  • Lehmann, E. L. (1953). The power of rank tests.The Annals of Mathematical Statistics, 24:23–43.

    Article  MATH  Google Scholar 

  • Lehmann, E. L. (1975).Nonparametrics: Statistical Methods Based on Ranks. Holden-Day Inc.

    Google Scholar 

  • Lehmann, E. L. (1983).Theory of Point Estimation. John Wiley & Sons.

    Google Scholar 

  • Lehmann, E. L. (1986).Testing Statistical Hypotheses. John Wiley & Sons.

    Google Scholar 

  • Lehmann, E. L. and Casella, G. (1998).Theory of Point Estimation. Springer-Verlag Inc.

    Google Scholar 

  • Lehmann, E. L. and Stein, C. (1949). On the theory of some non-parametric hypotheses.The Annals of Mathematical Statistics, 20:28–45.

    Article  MathSciNet  Google Scholar 

  • Leroux, B. G. and Puterman, M. L. (1992). Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models.Biometrics, 48:545–558.

    Article  Google Scholar 

  • Liang, K.-Y. (1985). Odds ratio inference with dependent data.Biometrika, 72:678–682.

    Article  Google Scholar 

  • Liang, K.-Y. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models.Biometrika, 73:13–22.

    Article  MATH  MathSciNet  Google Scholar 

  • Lindley, D. V. and Phillips, L. D. (1976). Inference for a Bernoulli process (A Bayesian view).The American Statistician, 30:112–119.

    MATH  MathSciNet  Google Scholar 

  • Lindsay, B. G. (1994). Efficiency versus robustness: The case for minimum Hellinger distance and related methods.The Annals of Statistics, 22:1081–1114.

    Article  MATH  MathSciNet  Google Scholar 

  • Lindsay, B. G. and Qu, A. (2003). Inference functions and quadratic score tests.Statistical Science, 18(3):394–410.

    Article  MATH  MathSciNet  Google Scholar 

  • Little, R. J. A. and Rubin, D. B. (1987).Statistical Analysis with Missing Data. J. Wiley & Sons.

    Google Scholar 

  • Liu, R. Y. and Singh, K. (1987). On a partial correction by the bootstrap.The Annals of Statistics, 15:1713–1718.

    Article  MATH  MathSciNet  Google Scholar 

  • Liu, X. and Shao, Y. (2003). Asymptotics for likelihood ratio tests under loss of identifiability.The Annals of Statistics, 31(3):807–832.

    Article  MATH  MathSciNet  Google Scholar 

  • Loh, W.-Y. (1987). Calibrating confidence coefficients.Journal of the American Statistical Association, 82:155–162.

    Article  MATH  MathSciNet  Google Scholar 

  • Magee, L. (1990).R 2 measures based on Wald and likelihood ratio joint significance tests.The American Statistician, 44:250–253.

    Google Scholar 

  • Mahfoud, Z. R. and Randles, R. H. (2005). Practical tests for randomized complete block designs.Journal of Multivariate Analysis, 96(1):73–92.

    Article  MATH  MathSciNet  Google Scholar 

  • Makelainen, T., Schmidt, K., and Styan, G. P. H. (1981). On the existence and uniqueness of the maximum-likelihood estimate of a vector-valued parameter in fixed-size samples.Annals of Statistics, 9:758–767.

    Article  MathSciNet  Google Scholar 

  • Mancl, L. A. and DeRouen, T. A. (2001). A covariance estimator for GEE with improved small-sample properties.Biometrics, 57(1):126–134.

    Article  MATH  MathSciNet  Google Scholar 

  • Mann, H. B. and Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other.The Annals of Mathematical Statistics, 18:50–60.

    Article  MATH  MathSciNet  Google Scholar 

  • McCullagh, P. (1983). Quasi-likelihood functions.The Annals of Statistics, 11:59–67.

    Article  MATH  MathSciNet  Google Scholar 

  • McCullagh, P. (1997). Linear models, vector spaces, and residual likelihood. In Gregoire, T. G., Brillinger, D. R., Diggle, P. J., Russek-Cohen, E., Warren, W. G., and Wolfinger, R. D., editors,Modelling Longitudinal and Spatially Correlated Data: Methods, Applications, and Future Directions. Lecture Notes in Statistics, Vol. 122, pages 1–10. Springer-Verlag Inc.

    Google Scholar 

  • McLachlan, G.J. & Krishnan, T. (1997).The EM Algorithm and Extensions. J. Wiley & Sons.

    Google Scholar 

  • Mehra, K. L. and Sarangi, J. (1967). Asymptotic efficiency of certain rank tests for comparative experiments.The Annals of Mathematical Statistics, 38:90–107.

    Article  MATH  MathSciNet  Google Scholar 

  • Memon, M. A., Cooper, N. J., Memon, B., Memon, M. I., and Abrams, K. R. (2003). Meta-analysis of randomized clinical trials comparing open and laparoscopic inguinal hernia repair.British Journal of Surgery, 90:1479–1492.

    Article  Google Scholar 

  • Messig, M. A. and Strawderman, W. E. (1993). Minimal sufficiency and completeness for dichotomous quantal response models.The Annals of Statistics, 21:2149–2157.

    Article  MATH  MathSciNet  Google Scholar 

  • Miller, R. G., J. (1974). An unbalanced jackknife.The Annals of Statistics, 2:880–891.

    Google Scholar 

  • Miller, J. J. (1977). Asymptotic properties of maximum likelihood estimates in the mixed model of the analysis of variance.The Annals of Statistics, 5:746–762.

    Article  MATH  MathSciNet  Google Scholar 

  • Miller, R. G. (1980). Combining 2 ×2 contingency tables. In Miller, R. G. e., Efron, B. e., Brown, B. W., J. e., and Moses, L. E. e., editors,Biostatistics Casebook, pages 73–83. John Wiley & Sons.

    Google Scholar 

  • Monahan, J. F. (2001).Numerical Methods of Statistics. Cambridge University Press.

    Google Scholar 

  • Monahan, J. F. and Boos, D. D. (1992). Proper likelihoods for Bayesian analysis.Biometrika, 79:271–278.

    Article  MATH  MathSciNet  Google Scholar 

  • Moore, D. S. (1977). Generalized inverses, Wald’s method, and the construction of chi-squared tests of fit.Journal of the American Statistical Association, 72:131–137.

    Article  MATH  MathSciNet  Google Scholar 

  • Moore, D. S. (1986). Tests of chi-squared type. In D’Agostino, R. B. and Stephens, M. A., editors,Goodness-of-fit techniques, pages 63–95. Marcel Dekker Inc.

    Google Scholar 

  • Nation, J. R., Bourgeois, A. E., Clark, D. E., Baker, D. M., and Hare, M. F. (1984). The effects of oral cadmium exposure on passive avoidance performance in the adult rat.Toxicology Letters, 20:41–47.

    Article  Google Scholar 

  • Nelder, J. A. and Wedderburn, R. W. M. (1972). Generalized linear models.Journal of the Royal Statistical Society, Series A: General, 135:370–384.

    Article  Google Scholar 

  • Neyman, J. and Pearson, E. S. (1928). On the use and interpretation of certain test criteria for purposes of statistical inference.Biometrika, 20A:175–240, 263–294.

    Google Scholar 

  • Neyman, J. and Pearson, E. S. (1933). On the problem of the most efficient tests of statistical hypotheses.Philosophical Transactions of the Royal Society of London, Ser. A, 231:289–337.

    Google Scholar 

  • Neyman, J. and Scott, E. L. (1948). Consistent estimates based on partially consistent observations.Econometrica, 16:1–32.

    Article  MathSciNet  Google Scholar 

  • Noether, G. E. (1949). On a theorem by wald and wolfowitz.The Annals of Mathematical Statistics, 20:455–458.

    Article  MATH  MathSciNet  Google Scholar 

  • Noether, G. E. (1955). On a theorem of pitman.The Annals of Mathematical Statistics,, 26:64–68.

    Article  MATH  MathSciNet  Google Scholar 

  • Noether, G. E. (1987). Sample size determination for some common nonparametric tests.Journal of the American Statistical Association, 82:645–647.

    Article  MATH  MathSciNet  Google Scholar 

  • O’Gorman, T. W. (2001). A comparison of the F-test, Friedman’s test, and several aligned rank tests for the analysis of randomized complete blocks.Journal of Agricultural, Biological, and Environmental Statistics, 6(3):367–378.

    Article  Google Scholar 

  • Olshen, R. A. (1967). Sign and Wilcoxon tests for linearity.The Annals of Mathematical Statistics, 38:1759–1769.

    Article  MATH  MathSciNet  Google Scholar 

  • Pace, L. and Salvan, A. (1997).Principles of Statistical Inference: from a Neo-Fisherian Perspective. World Scientific Publishing Company.

    Google Scholar 

  • Pirazzoli, P. A. (1982). Maree estreme a venezia (periodo 1872-1981).Acqua Aria, 10:1023–1029.

    Google Scholar 

  • Pitman, E. J. G. (1936). Sufficient statistics and intrinsic accuracy.Proc. Camb. Phil. Soc., 32:567–579.

    Article  Google Scholar 

  • Pitman, E. J. G. (1937a). Significance tests which may be applied to samples from any populations.Supplement to the Journal of the Royal Statistical Society, 4:119–130.

    Article  Google Scholar 

  • Pitman, E. J. G. (1937b). Significance tests which may be applied to samples from any populations. ii. the correlation coefficient test.Supplement to the Journal of the Royal Statistical Society, 4:225–232.

    Google Scholar 

  • Pitman, E. J. G. (1938). Significance tests which may be applied to samples from any populations. iii. the analysis of variance test.Biometrika, 29:322–335.

    Google Scholar 

  • Pitman, E. J. G. (1948).Notes on Non-Parametric Statitistical Inference. Columbia University (duplicated).

    Google Scholar 

  • Portnoy, S. (1988). Asymptotic behavior of likelihood methods for exponential families when the number of parameters tends to infinity.The Annals of Statistics, 16:356–366.

    Article  MATH  MathSciNet  Google Scholar 

  • Pratt, J. W. and Gibbons, J. D. (1981).Concepts of Nonparametric Theory. Springer-Verlag Inc.

    Google Scholar 

  • Prentice, R. L. (1988). Correlated binary regression with covariates specific to each binary observation.Biometrics, 44:1033–1048.

    Article  MATH  MathSciNet  Google Scholar 

  • Presnell, B. and Boos, D. D. (2004). The ios test for model misspecification.Journal of the American Statistical Association, 99(465):216–227.

    Article  MATH  MathSciNet  Google Scholar 

  • Puri, M. L. and Sen, P. K. (1971).Nonparametric Methods in Multivariate Analysis. John Wiley & Sons.

    Google Scholar 

  • Pyke, R. (1965). Spacings (with discussion).Journal of the Royal Statistical Society, Series B: Statistical Methodology, 27:395–449.

    MATH  MathSciNet  Google Scholar 

  • Qu, A., Lindsay, B. G., and Li, B. (2000). Improving generalised estimating equations using quadratic inference functions.Biometrika, 87(4):823–836.

    Article  MATH  MathSciNet  Google Scholar 

  • Quenouille, M. H. (1949). Approximate use of correlation in time series.Journal of the Royal Statistical Society, Series B, 11:18–84.

    MathSciNet  Google Scholar 

  • Quenouille, M. H. (1956). Notes on bias in estimation.Biometrika, 43:353–360.

    Article  MATH  MathSciNet  Google Scholar 

  • Quesenberry, C. P. (1975). Transforming samples from truncation parameter distributions to uniformity.Communications in Statistics, 4:1149–1156.

    Article  MathSciNet  Google Scholar 

  • Radelet, M. L. and Pierce, G. L. (1991). Choosing those who will die: race and the death penalty in florida.Florida Law Review, 43:1–34.

    Google Scholar 

  • Randles, R. H. (1982). On the asymptotic normality of statistics with estimated parameters.Annals of Statistics, 10:462–474.

    Article  MATH  MathSciNet  Google Scholar 

  • Randles, R. H. and Wolfe, D. A. (1979).Introduction to the Theory of Nonparametric Statistics. John Wiley & Sons.

    Google Scholar 

  • Randolph, P. A., Randolph, J. C., Mattingly, K., and Foster, M. M. (1977). Energy costs of reproduction in the cotton rat sigmodon hispidus.Ecology, 58:31–45.

    Article  Google Scholar 

  • Rao, C. R. (1948). Large sample tests of statistical hypotheses concerning several parameters with application to problems of estimation.Proceedings of the Cambridge Philosophical Society, 44:50–57.

    Article  MATH  Google Scholar 

  • Rao, C. R. (1973).Linear Statistical Inference and Its Applications. John Wiley & Sons.

    Google Scholar 

  • Rao, C. R. and Wu, Y. (2001). On model selection (Pkg: P1-64). InModel selection [Institute of Mathematical Statistics lecture notes-monograph series 38], pages 1–57. IMS Press.

    Google Scholar 

  • Read, T. R. C. and Cressie, N. A. C. (1988).Goodness-of-fit Statistics for Discrete Multivariate Data. Springer-Verlag Inc.

    Google Scholar 

  • Reid, N. (1988). Saddlepoint methods and statistical inference (C/R: P228-238).Statistical Science, 3:213–227.

    Article  MATH  MathSciNet  Google Scholar 

  • Ridout, M., Hinde, J., and Demétrio, C. G. B. (2001). A score test for testing a zero-inflated Poisson regression model against zero-inflated negative binomial alternatives.Biometrics, 57(1):219–223.

    Article  MATH  MathSciNet  Google Scholar 

  • Robert, C. P. (2001).The Bayesian Choice: from Decision-theoretic Foundations to Computational Implementation. Springer-Verlag Inc.

    Google Scholar 

  • Roberts, M. E., Tchanturia, K., Stahl, D., Southgate, L., and Treasure, J. (2007). A systematic review and metaanalysis of set-shifting ability in eating disorders.Psychol. Med., 37:1075–1084.

    Article  Google Scholar 

  • Robertson, T., Wright, F. T., and Dykstra, R. (1988).Order Restricted Statistical Inference. John Wiley & Sons.

    Google Scholar 

  • Robins, J. M., van der Vaart, A., and Ventura, V.

    Google Scholar 

  • Robinson, J. (1980). An asymptotic expansion for permutation tests with several samples.The Annals of Statistics, 8:851–864.

    Article  MATH  MathSciNet  Google Scholar 

  • Rosen, O. and Cohen, A. (1995). Constructing a bootstrap confidence interval for the unknown concentration in radioimmunoassay (Disc: P953-953).Statistics in Medicine, 14:935–952.

    Article  Google Scholar 

  • Rotnitzky, A. and Jewell, N. P. (1990). Hypothesis testing of regression parameters in semiparametric generalized linear models for cluster correlated data.Biometrika, 77:485–497.

    Article  MATH  MathSciNet  Google Scholar 

  • Ruppert, D. (1987). What is kurtosis - an influence function-approach.American Statisitican, 41:1–5.

    MATH  MathSciNet  Google Scholar 

  • Sampson, A. R. (1974). A tale of two regressions.Journal of the American Statistical Association, 69:682–689.

    Article  MATH  MathSciNet  Google Scholar 

  • Santner, T. J. (1998). Teaching large-sample binomial confidence intervals.Teaching Statistics, 20:20–23.

    Article  Google Scholar 

  • Savage, I. R. (1956). Contributions to the theory of rank order statistics-the two-sample case.The Annals of Mathematical Statistics, 27:590–615.

    Article  MATH  MathSciNet  Google Scholar 

  • Schrader, R. M. and Hettmansperger, T. P. (1980). Robust analysis of variance based upon a likelihood ratio criterion.Biometrika, 67:93–101.

    Article  MATH  MathSciNet  Google Scholar 

  • Schucany, W. R., Gray, H. L., and Owen, D. B. (1971). On bias reduction in estimation.Journal of the American Statistical Association, 66:524–533.

    Article  MATH  Google Scholar 

  • Schwarz, G. (1978). Estimating the dimension of a model.The Annals of Statistics, 6:461–464.

    Article  MATH  MathSciNet  Google Scholar 

  • Searle, S. R. (1971).Linear models. John Wiley & Sons.

    Google Scholar 

  • Seber, G. A. F. and Wild, C. J. (1989).Nonlinear Regression. John Wiley & Sons.

    Google Scholar 

  • Self, S. G. and Liang, K.-Y. (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions.Journal of the American Statistical Association, 82:605–610.

    Article  MATH  MathSciNet  Google Scholar 

  • Sen, P. K. (1968). On a class of aligned rank order tests in two-way layouts.The Annals of Mathematical Statistics, 39:1115–1124.

    Article  MATH  Google Scholar 

  • Sen, P. K. (1982). OnM tests in linear models.Biometrika, 69:245–248.

    MATH  MathSciNet  Google Scholar 

  • Serfling, R. J. (1980).Approximation Theorems of Mathematical Statistics. Wiley, New York.

    Book  MATH  Google Scholar 

  • Shanbhag, D. N. (1968). Some remarks concerning Khatri’s result on quadratic forms.Biometrika, 55:593–595.

    MATH  Google Scholar 

  • Shao, J. and Tu, D. (1995).The Jackknife and Bootstrap. Springer-Verlag Inc.

    Google Scholar 

  • Shao, J. and Wu, C. F. J. (1989). A general theory for jackknife variance estimation.The Annals of Statistics, 17:1176–1197.

    Article  MATH  MathSciNet  Google Scholar 

  • Sidik, K. and Jonkman, J. N. (2007). A comparison of heterogeneity variance estimators in combining results of studies.Statistics in Medicine, 26(9):1964–1981.

    Article  MathSciNet  Google Scholar 

  • Siegel, A. F. (1985). Modelling data containing exact zeroes using zero degrees of freedom.Journal of the Royal Statistical Society, Series B: Methodological, 47:267–271.

    MATH  MathSciNet  Google Scholar 

  • Silvapulle, M. J. and Sen, P. K. (2005).Constrained Statistical Inference: Inequality, Order, and Shape Restrictions. Wiley-Interscience.

    Google Scholar 

  • Simpson, D. G. (1987). Minimum Hellinger distance estimation for the analysis of count data.Journal of the American Statistical Association, 82:802–807.

    Article  MATH  MathSciNet  Google Scholar 

  • Singh, K. (1981). On the asymptotic accuracy of Efron’s bootstrap.The Annals of Statistics, 9:1187–1195.

    Article  MATH  MathSciNet  Google Scholar 

  • Smith, R. L. (1985). Maximum likelihood estimation in a class of nonregular cases.Biometrika, 72:67–90.

    Article  MATH  MathSciNet  Google Scholar 

  • Smith, T. C., Spiegelhalter, D. J., and Thomas, A. (1995). Bayesian approaches to random-effects meta-analysis: A comparative study.Statistics in Medicine, 14:2685–2699.

    Article  Google Scholar 

  • Stacy, E. W. (1962). A generalization of the gamma distribution.The Annals of Mathematical Statistics, 33:1187–1191.

    Article  MATH  MathSciNet  Google Scholar 

  • Stefanski, L. A. and Boos, D. D. (2002). The calculus of M-estimation.The American Statistician, 56(1):29–38.

    Article  MathSciNet  Google Scholar 

  • Stefanski, L. A. and Carroll, R. J. (1987). Conditional scores and optimal scores for generalized linear measurement-error models.Biometrika, 74:703–716.

    MATH  MathSciNet  Google Scholar 

  • Stefanski, L. A. and Cook, J. R. (1995). Simulation-extrapolation: The measurement error jackknife.Journal of the American Statistical Association, 90:1247–1256.

    Article  MATH  MathSciNet  Google Scholar 

  • Stephens, M. A. (1977). Goodness of fit for the extreme value distribution.Biometrika, 64:583–588.

    Article  MATH  MathSciNet  Google Scholar 

  • Student (Gosset, W. S. (1908). The probable error of a mean.Biometrika, 6(1):1–25.

    Google Scholar 

  • Styan, G. P. H. (1970). Notes on the distribution of quadratic forms in singular normal variables.Biometrika, 57:567–572.

    Article  MATH  Google Scholar 

  • Suissa, S. and Shuster, J. J. (1985). Exact unconditional sample sizes for the 2 by 2 binomial trial.Journal of the Royal Statistical Society, Series A: General, 148:317–327.

    Article  MATH  MathSciNet  Google Scholar 

  • Tanner, M. A. and Wong, W. H. (1987). The calculation of posterior distributions by data augmentation (C/R: P541-550).Journal of the American Statistical Association, 82:528–540.

    Article  MATH  MathSciNet  Google Scholar 

  • Tarone, R. E. (1979). Testing the goodness of fit of the binomial distribution (Corr: V77 p668).Biometrika, 66:585–590.

    Article  MATH  Google Scholar 

  • Tarone, R. E. and Gart, J. J. (1980). On the robustness of combined tests for trends in proportions.Journal of the American Statistical Association, 75:110–116.

    Article  MATH  Google Scholar 

  • Teo, K. K., Yusuf, S., Collins, R., Held, P. H., and Peto, R. (1991). Effects of intravenous magnesium in suspected acute myocardial infarction: Overview of randomised trials.British Medical Journal, 303:1499–1503.

    Article  Google Scholar 

  • Thompson, G. L. (1991). A note on the rank transform for interactions (Corr: 93V80 p711).Biometrika, 78:697–701.

    Article  MATH  MathSciNet  Google Scholar 

  • Tobin, J. (1958). Estimation of relationships for limited dependent-variables.Econometrica, 26:24–36.

    Article  MATH  MathSciNet  Google Scholar 

  • Tsiatis, A. A. and Davidian, M. (2001). A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error.Biometrika, 88:447–458.

    Article  MATH  MathSciNet  Google Scholar 

  • Tukey, J. (1958). Bias and confidence in not quite large samples (abstract).The Annals of Mathematical Statistics, 29:614–614.

    Article  Google Scholar 

  • van den Broek, J. (1995). A score test for zero inflation in a Poisson distribution.Biometrics, 51:738–743.

    Article  MATH  MathSciNet  Google Scholar 

  • van der Vaart, A. W. (1998).Asymptotic Statistics. Cambridge University Press.

    Google Scholar 

  • van Elteren, P. H. (1960). On the combination of independent two-sample tests of wilcoxon.Bulletin of the International Statistical Institute, 37:351–361.

    MATH  Google Scholar 

  • van Elteren, P. H. and Noether, G. E. (1959). The asymptotic efficiency of the χ r 2-test for a balanced incomplete block design.Biometrika, 46:475–477.

    Article  MATH  Google Scholar 

  • Venables, W. N. and Ripley, B. D. (1997).Modern Applied Statistics with S-Plus. Springer-Verlag Inc.

    Google Scholar 

  • Verbeke, G. and Molenberghs, G. (2003). The use of score tests for inference on variance components.Biometrics, 59(2):254–262.

    Article  MATH  MathSciNet  Google Scholar 

  • von Mises, R. (1947). On the asymptotic distribution of differentiable statistical functions.The Annals of Mathematical Statistics, 18:309–348.

    Article  MATH  Google Scholar 

  • Wainer, H. (1993). Tabular presentation.Chance, 6(3):52–56.

    Google Scholar 

  • Wainer, H. (1997a). Improving tabular displays, with NAEP tables as examples and inspirations.Journal of Educational and Behavioral Statistics, 22:1–30.

    Article  Google Scholar 

  • Wainer, H. (1997b).Visual Revelations: Graphical Tales of Fate and Deception from Napoleon Bonaparte to Ross Perot. Springer-Verlag Inc.

    Google Scholar 

  • Wald, A. (1943). Tests of statistical hypotheses concerning several parameters when the number of observations is large.Transactions of the American Mathematical Society, 54(3):426–482.

    Article  MATH  MathSciNet  Google Scholar 

  • Wald, A. (1949). Note on the consistency of maximum likelihood estimate.The Annals of Mathematical Statistics, 20:595–601.

    Article  MATH  MathSciNet  Google Scholar 

  • Wald, A. and Wolfowitz, J. (1944). Statistical tests based on permutations of the observations.The Annals of Mathematical Statistics,, 15:358–372.

    Article  MATH  MathSciNet  Google Scholar 

  • Warn, D. E., Thompson, S. G., and Spiegelhalter, D. J. (2002). Bayesian random effects meta-analysis of trials with binary outcomes: Methods for the absolute risk difference and relative risk scales.Statistics in Medicine, 21(11):1601–1623.

    Article  Google Scholar 

  • Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method.Biometrika, 61:439–447.

    MATH  MathSciNet  Google Scholar 

  • Weir, B. S. (1996).Genetic Data Analysis 2: Methods for Discrete Population Genetic Data. Sunderland: Sinauer Associates.

    Google Scholar 

  • Welch, B. L. (1937). On the z-test in randomized blocks and latin squares.Biometrika, 29:21–52.

    Article  MATH  Google Scholar 

  • Welch, W. J. (1987). Rerandomizing the median in matched-pairs designs.Biometrika, 74:609–614.

    Article  MathSciNet  Google Scholar 

  • White, H. (1981). Consequences and detection of misspecified nonlinear regression models.Journal of the American Statistical Association, 76:419–433.

    Article  MATH  MathSciNet  Google Scholar 

  • White, H. (1982). Maximum likelihood estimation of misspecified models.Econometrica, 50:1–26.

    Article  MATH  MathSciNet  Google Scholar 

  • Wilcoxon, F. (1945). Individual comparisons by ranking methods.Biometrics Bulletin, 6:80–83.

    Article  Google Scholar 

  • Wilks, S. S. (1938). The large-sample distribution of the likelihood ratio for testing composite hypotheses.Annals of Mathematical Statistics, 9:60–62.

    Article  Google Scholar 

  • Wilson, D. H. (2002).Signed Scale Measures: An Introduction and Application. Ph.D Thesis, NC State University.

    Google Scholar 

  • Wu, C. F. J. (1983). On the convergence properties of the EM algorithm.The Annals of Statistics, 11:95–103.

    Article  MATH  MathSciNet  Google Scholar 

  • Wu, C. F. J. (1986). Jackknife, bootstrap and other resampling methods in regression analysis (C/R: P1295-1350; Ref: V16 p479).The Annals of Statistics, 14:1261–1295.

    Article  MATH  MathSciNet  Google Scholar 

  • Wu, C.-t., Gumpertz, M. L., and Boos, D. D. (2001). Comparison of GEE, MINQUE, ML, and REML estimating equations for normally distributed data.The American Statistician, 55(2):125–130.

    Google Scholar 

  • Zehna, P. W. (1966). Invariance of maximum likelihood estimations.The Annals of Mathematical Statistics, 37:744–744.

    Article  MATH  MathSciNet  Google Scholar 

  • Zeng, Q. and Davidian, M. (1997). Bootstrap-adjusted calibration confidence intervals for immunoassay.Journal of the American Statistical Association, 92:278–290.

    Article  MATH  MathSciNet  Google Scholar 

  • Zhang, J. and Boos, D. D. (1994). Adjusted power estimates in Monte Carlo experiments.Communications in Statistics: Simulation and Computation, 23:165–173.

    Article  MATH  Google Scholar 

  • Zhang, J. and Boos, D. D. (1997). Mantel-Haenszel test statistics for correlated binary data.Biometrics, 53:1185–1198.

    Article  MATH  MathSciNet  Google Scholar 

  • Zhao, L. P. and Prentice, R. L. (1990). Correlated binary regression using a quadratic exponential model.Biometrika, 77:642–648.

    Article  MathSciNet  Google Scholar 

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Boos, D.D., Stefanski, L.A. (2013). M-Estimation (Estimating Equations). In: Essential Statistical Inference. Springer Texts in Statistics, vol 120. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4818-1_7

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