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Risk Estimation

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References

  • Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Proceedings of the Second International Symposium on Information Theory, pp. 267–281, B.N. Petrov and F. Caski, eds. Akademiai Kiado, Budapest.

    Google Scholar 

  • Barron, A., Birgé, L., and Massart, P. (1999). Risk bounds for model selection by penalization. Probability Theory and Related Fields, 113:301–413.

    Article  Google Scholar 

  • Birman, M. S. and Solomjak, M. Z. (1967). Piecewise polynomial approximations of functions in the class \(w_p^\alpha\). Matematicheskii Sbornik, 73:331–355.

    Google Scholar 

  • Braga-Neto, U., Hashimoto, R., Dougherty, E. R., and Carroll, R. J. (2004). Is cross-validation better than resubstitution for ranking genes? Bioinformatics, 20:253–258.

    Article  PubMed  CAS  Google Scholar 

  • Braga-Neto, U. M. and Dougherty, E. R. (2004). Is cross-validation valid for small-sample microarray classification? Bioinformatics, 20:374–380.

    Article  PubMed  CAS  Google Scholar 

  • Bregman, L. M. (1967). The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming. USSR Computational Mathematics and Mathematical Physics, 7:200–217.

    Article  Google Scholar 

  • Breiman, L. (1992). The little bootstrap and other methods for dimensionality selection in regression: X-fixed prediction error. Journal of the American Statistical Association, 87:735–754.

    Article  Google Scholar 

  • Brown, L. D. (1986). Fundamentals of Statistical Exponential Families. IMS Lecture Notes Monograph, Hayward.

    Google Scholar 

  • Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Multimodel Inference: A Practical Information – Theoretic Approach, 2nd edn. Springer, New York.

    Google Scholar 

  • Candès, E. J. (2006). Modern statistical estimation via oracle inequalities. Acta Numerica, 15:257–325.

    Article  Google Scholar 

  • Cavanaugh, J. E. and Shumway, R. H. (1997). A bootstrap variant of aic for state-space model selection. Statistica Sinica, 7:473–496.

    Google Scholar 

  • Claeskens, G. and Hjort, N. L. (2003). The focused information criterion. Journal of the American Statistical Association, 98:900–916.

    Article  Google Scholar 

  • Claeskens, G. and Carroll, R. J. (2007). An asymptotic theory for model selection inference in general semiparametric problems. Biometrika, 94:249–265.

    Article  Google Scholar 

  • Cox, D. (1975). Partial likelihood. Biometrika, 62:269–276.

    Article  Google Scholar 

  • DeVore, R. A. (1998). Nonlinear approximation. Acta Numerica, 7:51–150.

    Article  Google Scholar 

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

    Google Scholar 

  • Donohue, M., Xu, R., Gamst, A., Vaida, F., and Harrington, D. P. (2007). Model selection under the proportional hazards mixed-effects model. Proceedings of the 2007 Joint Statistical Meetings, CD-ROM.

    Google Scholar 

  • Efron, B. (1982). The Jackknife, the Bootstrap and Other Resampling Plans. SIAM.

    Google Scholar 

  • Efron, B. (1983). Estimating the error rate of a prediction rule: Improvement on cross-validation. Journal of the American Statistical Association, 78:316–331.

    Article  Google Scholar 

  • Efron, B. (1986). How biased is the apparent error rate of a prediction rule? Journal of the American Statistical Association, 81:461–470.

    Article  Google Scholar 

  • Efron, B. (2004). The estimation of prediction error: Covariance penalties and cross-validation. Journal of the American Statistical Association, 99:619–642.

    Article  Google Scholar 

  • Fan, J. and Wong, W. H. (2000). Discussion of ‘On profile likelihood’, in Murphy, S. A. and van der Vaart, A. W., eds. Journal of the American Statistical Association, 95:468–471.

    Article  Google Scholar 

  • Feng, Z., Prentice, R., and Srivastava, S. (2004). Research issues and strategies for genomic and proteomic biomarker discovery and validation: a statistical perspective. Pharmacogenomics, 5:709–719.

    Article  PubMed  CAS  Google Scholar 

  • Fourdrinier, D., Strawderman, W. E., and Wells, M. T. (1998). On the construction of Bayes minimax estimators. Annals of Statistics, 26:660–671.

    Article  Google Scholar 

  • Hajek, J., Sidak, Z., and Sen, P. K. (1999). The Theory of Rank Tests, 2nd edn. Academic Press, New York.

    Google Scholar 

  • Hand, D. J. (2006). Classifier technology and the illusion of progress. Statistical Science, 21:1–14.

    Article  Google Scholar 

  • Hastie, T. and Tibshirani, R. (1990). Generalized Linear Models. Chapman & Hall, London.

    Google Scholar 

  • Hastie, T., Tibshirani, R., and Friedman, J. (2001). The Elements of Statistical Learning. Springer, New York.

    Google Scholar 

  • Hjort, N. L. and Claeskens, G. (2003). Frequentist model average estimators. Journal of the American Statistical Association, 98:879–899.

    Article  Google Scholar 

  • Hodges, J. S. and Sargent, D. J. (2001). Counting degrees of freedom in hierarchical and other richly parameterized models. Biometrika, 88(2):367–279.

    Article  Google Scholar 

  • Johnstone, I. M. (2002). Function estimation and gaussian sequence models. http://www-stat.stanford.edu/ĩmj/baseb.pdf.

  • Lu, X., Gamst, A., and Xu, R. (2007). On gene discovery and rediscovery. In Proceedings of the 2007 Joint Statistical Meetings. CD-ROM.

    Google Scholar 

  • Mallows, C. L. (1973). Some comments on C p . Technometrics, 15:661–675.

    Article  Google Scholar 

  • Mammen, E. and van de Geer, S. (1997). Local adaptive regression splines. Annals of Statistics, 25:387–413.

    Article  Google Scholar 

  • Natarajan, B. K. (1995). Sparse approximate solutions to linear systems. SIAM Journal on Computing, 24:227–234.

    Article  Google Scholar 

  • Pan, W. (1999). Bootstrapping likelihood for model selection with small samples. Journal of Computational and Graphical Statistics, 8:687–698.

    Article  Google Scholar 

  • Pan, W. (2001). Model selection in estimating equations. Biometrics, 57:120–125.

    Article  PubMed  CAS  Google Scholar 

  • Romano, J. P. (1990). On the behavior of randomization tests without a group invariance assumption. Journal of the American Statistical Association, 85:686–692.

    Article  Google Scholar 

  • Severini, T. A. and Wong, W. H. (1992). Profile likelihood and conditionally parametric models. Annals of Statistics, 20:1768–1802.

    Article  Google Scholar 

  • Shang, J. and Cavanaugh, J. E. (2008). Bootstrap variants of the Akaike information criterion for mixed model selection. Computational Statistics and Data Analysis, 52:2004–2021.

    Article  Google Scholar 

  • Shen, X. and Ye, J. (2002). Adaptive model selection. Journal of the American Statistical Association, 97:210–221.

    Article  Google Scholar 

  • Shen, X., Huang, H., and Ye, J. (2004). Comment to Efron (2004). Journal of the American Statistical Association, 99:634–637.

    Article  Google Scholar 

  • Shibata, R. (1997). Bootstrap estimate of Kullback-Leibler information for model selection. Statistica Sinica, 7:375–394.

    Google Scholar 

  • Silverman, B. W. (1984). Spline smoothing: The equivalent kernel method. Annals of Statistics, 12:898–916.

    Article  Google Scholar 

  • Stein, C. (1973). Estimation of the mean of a multivariate normal distribution. Proceedings of Prague Symposium on Asymptotic Statistics, pp. 345–381.

    Google Scholar 

  • Stein, C. (1981). Estimation of the mean of a multivariate normal distribution. Annals of Statistics, 9:1135–1151.

    Article  Google Scholar 

  • Strawderman, W. E. (1971). Proper Bayes minimax estimators of the multivariate normal mean. Annals of Mathematical Statistics, 42:385–388.

    Article  Google Scholar 

  • Tukey, J. W. (1961). Curves as parameters and touch estimation. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability.

    Google Scholar 

  • Vaida, F. and Blanchard, S. (2005). Conditional Akaike information for mixed-effects models. Biometrika, 92:351–370.

    Article  Google Scholar 

  • van der Vaart, A. W. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes. Springer, New York.

    Google Scholar 

  • Vuong, Q. H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica, 57:307–333.

    Article  Google Scholar 

  • Xu, R. and Li, X. (2003). A comparison of parametric versus permutation methods with applications to general and temporal microarray gene expression data. Bioinformatics, 19:1284–1289.

    Article  PubMed  CAS  Google Scholar 

  • Xu, R., Vaida, F., and Harrington, D. (2008). Using profile likelihood for semiparametric model selection with application to proportional hazards mixed models. Statistica Sinica, in press.

    Google Scholar 

  • Ye, J. (1998). On meausuring and correcting the effects of data mining and model selection. Journal of the American Statistical Association, 93:120–131.

    Article  Google Scholar 

  • Zhang, C. (2004). Comment to Efron (2004). Journal of the American Statistical Association, 99:637–640.

    Article  Google Scholar 

  • Zhang, C., Lu, X., and Zhang, X. (2006). Significance of gene ranking for classification of microarray samples. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 3:312–320.

    Article  PubMed  CAS  Google Scholar 

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Xu, R., Gamst, A. (2009). Risk Estimation. In: Li, X., Xu, R. (eds) High-Dimensional Data Analysis in Cancer Research. Applied Bioinformatics and Biostatistics in Cancer Research. Springer, New York, NY. https://doi.org/10.1007/978-0-387-69765-9_4

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