Model selection and model averaging

Model Selection and Model Averaging

Volumn , Issue , 2008, Pages 1-312

  Claeskens, Gerda ^a   Hjort, Nils Lid ^b  

^a Katholieke Universiteit Leuven   (Belgium)

^b UNIVERSITY OF OSLO   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84924487463     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511790485     Document Type: Book

References (294)

1. Aalen, O. O. and Gjessing, H. (2001). Understanding the shape of the hazard rate: a process point of view. Statistical Science,16:1-22.
2. Abramovich, F. and Benjamini, Y. (1996). Adaptive thresholding of wavelet coefficients. Computational Statistics and Data Analysis,22:351-361.
3. Abramovich, F., Sapatinas, F. and Silverman, B. W. (1998). Wavelet thresholding via a Bayesian approach. Journal of the Royal Statistical Society, Series B,60:725-749.
4. Aerts, M., Claeskens, G. and Hart, J. D. (1999). Testing the fit of a parametric function. Journal of the American Statistical Association,94:869-879.
5. Aerts, M., Claeskens, G. and Hart, J. D. (2000). Testing lack of fit in multiple regression. Biometrika,87:405-424.
6. Aerts, M., Claeskens, G. and Hart, J. D. (2004). Bayesian-motivated tests of function fit and their asymptotic frequentist properties. The Annals of Statistics,32:2580-2615.
7. Agostinelli, C. (2002). Robust model selection in regression via weighted likelihood methodology. Statistics & Probability Letters,56:289-300.
8. Akaike, H. (1969). Fitting autoregressive models for prediction. Annals of the Institute of Statistical Mathematics,21:243-247.
9. Akaike, H. (1970). Statistical predictor identification. Annals of the Institute of Statistical Mathematics,22:203-217.
10. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Petrov, B. and Csáki, F. (editors), Second International Symposium on Information Theory, pages 267-281. Akadémiai Kiadó, Budapest.
11. Akaike, H. (1977). On entropy maximization principle. In Applications of Statistics (Proceedings of Symposium, Wright State University, Dayton, Ohio, 1976), pages 27-41. North-Holland, Amsterdam.
12. Akaike, H. (1978). A new look at the Bayes procedure. Biometrika,65:53-59.
13. Allen, D. M. (1974). The relationship between variable selection and data augmentation and a method for prediction. Technometrics,16:125-127.
14. Andersen, P. K., Borgan, Ø., Gill, R. D. and Keiding, N. (1993). Statistical Models Based on Counting Processes. Springer-Verlag, New York.
15. Antoniadis, A., Gijbels, I. and Grégoire, G. (1997). Model selection using wavelet decomposition and applications. Biometrika,84:751-763.
16. Augustin, N. H., Sauerbrei, W. and Schumacher, M. (2005). The practical utility of incorporating model selection uncertainty into prognostic models for survival data. Statistical Modelling, 5:95-118.
17. Bai, Z. D., Rao, C. R. and Wu, Y. (1999). Model selection with data-oriented penalty. Journal of Statistical Planning and Inference,77:103-117.
18. Barndorff-Nielsen, O. E. and Cox, D. R. (1994). Inference and Asymptotics, Vol. 52. Chapman & Hall, London.
19. Basu, A., Harris, I. R., Hjort, N. L. and Jones, M. C. (1998). Robust and efficient estimation by minimising a density power divergence. Biometrika,85:549-559.
20. Benjamini, Y. and 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.
21. Berger, J. (1982). Estimation in continuous exponential families: Bayesian estimation subject to risk restrictions and inadmissibility results. In Statistical Decision Theory and Related Topics, III, Vol. 1 (West Lafayette, Indiana, 1981), pages 109-141. Academic Press, New York.
22. Berger, J. O. and Pericchi, L. R. (1996). The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association,91:109-122.
23. Berger, J. O. and Pericchi, L. R. (2001). Objective Bayesian methods for model selection: introduction and comparions. In Lahiri, P. (editor), Model Selection, IMS Lecture Notes - Monograph Series, pages 135-207. IMS, Beechwood, Ohio.
24. Bernstein, F. (1924). Ergebnisse einer biostatistichen zusammenfassenden Betrachtung iiber die erblichen Blutstrukturen des Menschen. Klinische Wochenschriften,3:1467-1495.
25. Bickel, P. J. (1981). Minimax estimation of the mean of a normal distribution when the parameter space is restricted. The Annals of Statistics,9:1301-1309.
26. Bickel, P. J. (1983). Minimax estimation of the mean of a normal distribution subject to doing well at a point. In Recent Advances in Statistics, pages 511-528. Academic Press, New York.
27. Bickel, P. J. (1984). Parametric robustness: small biases can be worthwhile. The Annals of Statistics,12:864-879.
28. Bickel, P. J. and Doksum, K. A. (2001). Mathematical Statistics: Basic Ideas and Selected Topics, Vol. I (2nd edition). Prentice-Hall, London.
29. Bøvelstad, H. M., Nygard, S., Størvold, H. L., Aldrin, M., Borgan, Ø., Frigessi, A. and Lingjsrde, O. C. (2007). Predicting survival from microarray data - a comparative study. Bioinformatics, 23:2080-2087.
30. Bozdogan, H. (1987). Model selection and Akaike’s information criterion (AIC): the general theory and its analytical extensions. Psychometrika,52:345-370.
31. Bozdogan, H., Sclove, S. L. and Gupta, A. K. (1994). AIC-replacements for some multivariate tests of homogeneity with applications in multisample clustering and variable selection. In Proceedings of the First US/Japan Conference on the Frontiers of Statistical Modeling: An Informational Approach, Vol. 2 (Knoxville, Tennessee, 1992), pages 19-20. 199-232. Kluwer Academic Publishers, Dordrecht.
32. Breiman, L. (1992). The little bootstrap and other methods for dimensionality selection in regression: X-fixed prediction error. Journal of the American Statistical Association,87:738-754.
33. Breiman, L. (1995). Better subset regression using the nonnegative garrote. Technometrics, 37:373-384.
34. Breiman, L. (2001). Statistical modeling: the two cultures. Statistical Science,16:199-231. With discussion and a rejoinder by the author.
35. Breiman, L. and Freedman, D. (1983). How many variables should be entered in a regression equation? Journal of the American Statistical Association,78:131-136.
36. Brockwell, P. J. and Davis, R. A. (1991). Time Series: Theory and Methods (2nd edition). Springer- Verlag, New York.
37. Brockwell, P. J. and Davis, R. A. (2002). Introduction to Time Series and Forecasting (2nd edition). Springer-Verlag, New York.
38. Buckland, S. T., Burnham, K. P. and Augustin, N. H. (1997). Model selection: an integral part of inference. Biometrics,53:603-618.
39. Bueso, M. C., Qian, G. and Angulo, J. M. (1999). Stochastic complexity and model selection from incomplete data. Journal of Statistical Planning and Inference,76:273-284.
40. Bunea, F. and McKeague, I. W. (2005). Covariate selection for semiparametric hazard function regression models. Journal of Multivariate Analysis,92:186-204.
41. Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (2nd edition). Springer-Verlag, New York.
42. Candes, E. and Tao, T. (2008). The Dantzig selector: statistical estimation when p is much larger than n. Annals of Statistics,35:2313-2351.
43. Carroll, R. J. and Ruppert, D. (1988). Transformation and Weighting in Regression. Chapman & Hall, London.
44. Cavanaugh, J. E. and Shumway, R. H. (1998). An Akaike information criterion for model selection in the presence of incomplete data. Journal of Statistical Planning and Inference,67:45-65.
45. Celeux, G., Forbes, F., Robert, C. and Titterington, D. (2006). Deviance information criteria for missing data models. Bayesian Analysis,1(4):651-705.
46. Chatfield, C. (1995). Model uncertainty, data mining and statistical inference. Journal of the Royal Statistical Society, Series A,158:419-466.
47. Chatfield, C. (2004). The Analysis of Time Series (6th edition). Chapman & Hall/CRC, Boca Raton, Florida.
48. Chipman, H., George, E. I. and McCulloch, R.E. (2001). The practical implementation of Bayesian model selection. In Model Selection, IMS Lecture Notes - Monograph Series, pages 65-134. Institute of Mathematical Statistics, Beechwood, Ohio.
49. Chipman, H., Kolaczyk, E. and McCulloch, R. (1997). Adaptive Bayesian wavelet shrinkage. Journal of the American Statistical Association,92:1413-1421.
50. Choi, B. S. (1992). ARMA Model Identification. Springer-Verlag, New York.
51. Choi, E., Hall, P. and Presnell, B. (2000). Rendering parametric procedures more robust by empirically tilting the model. Biometrika,87:453-465.
52. Claeskens, G. (2004). Restricted likelihood ratio lack of fit tests using mixed spline models. Journal of the Royal Statistical Society, Series B,66:909-926.
53. Claeskens, G. and Carroll, R. (2007). An asymptotic theory for model selection inference in general semiparametric problems. Biometrika,2:249-265.
54. Claeskens, G. and Consentino, F. (2008). Variable selection with incomplete covariate data. Biometrics,64, to appear.
55. Claeskens, G., Croux, C. and Van Kerckhoven, J. (2006). Variable selection for logistic regression using a prediction focussed information criterion. Biometrics,62:972-979.
56. Claeskens, G., Croux, C. and Van Kerckhoven, J. (2007). Prediction focussed model selection for autoregressive models. The Australian and New Zealand Journal of Statistics,49(4):359-379.
57. Claeskens, G. and Hjort, N. L. (2003). The focused information criterion. Journal of the American Statistical Association,98:900-916. With discussion and a rejoinder by the authors.
58. Claeskens, G. and Hjort, N. L. (2004). Goodness of fit via nonparametric likelihood ratios. Scandinavian Journal of Statistics,31:487-513.
59. Claeskens, G. and Hjort, N. L. (2008). Minimising average risk in regression models. Econometric Theory, 24:493-527.
60. Clyde, M. A. (1999). Bayesian model averaging and model search strategies. In Bayesian Statistics VI (Alcoceber, 1998), pages 157-185. Oxford University Press, Oxford.
61. Clyde, M. A. and George, E. (2004). Model uncertainty. Statistical Science,19:81-94.
62. Cook, R. D. and Weisberg, S. (1994). An Introduction to Regression Graphics. John Wiley & Sons Inc., New York.
63. Cover, T. M. and Thomas, J. A. (1991). Elements of Information Theory. John Wiley & Sons Inc., New York.
64. Cox, D. R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society, Series B,34:187-220. With discussion.
65. de Rooij, S. and Griinwald, P. (2006). An empirical study of minimum description length model selection with infinite parametric complexity. Journal of Mathematical Psychology,50:180-192.
66. DeBlasi, P. and Hjort, N. L. (2007). Bayesian survival analysis in proportional hazard models with logistic relative risk. Scandinavian Journal of Statistics,34:229-257.
67. Dobson, A. (2002). An Introduction to Generalized Linear Models (2nd edition). CRC/Chapman & Hall.
68. Dominicus, A., Skrondal, A., Gjessing, H., Pedersen, N. and Palmgren, J. (2006). Likelihood ratio tests in behavioral genetics: problems and solutions. Behavior Genetics, 36:331-340.
69. Donoho, D. L. and Johnstone, I. M. (1994). Ideal spatial adaptation via wavelet shrinkage. Biometrika,81:425-455.
70. Donoho, D. L. and Johnstone, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. Journal of the American Statistical Association,90:1200-1224.
71. Draper, D. (1995). Assessment and propagation of model uncertainty. Journal of the Royal Statistical Society, Series B,57:45-97. With discussion and a reply by the author.
72. Efron, B. (1983). Estimating the error rate of a prediction rule: improvement on cross-validation. Journal of the American Statistical Association,78:316-331.
73. Efron, B. and Gous, A. (2001). Scales of evidence for model selection: Fisher versus Jeffreys. In Model Selection, IMS Lecture Notes - Monograph Series, pages 208-256. Institute of Mathematical Statistics, Beechwood, Ohio.
74. Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004). Least angle regression. The Annals of Statistics,32:407-499. With discussion and a rejoinder by the authors.
75. Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman & Hall, New York.
76. Eguchi, S. and Copas, J. (1998). A class of local likelihood methods and near-parametric asymptotics. Journal of the Royal Statistical Society, Series B,60:709-724.
77. Einstein, A. (1934). On the method of theoretical physics. The Philosophy of Science,1:163-169.
78. Eubank, R. L. and Hart, J. D. (1992). Testing goodness-of-fit in regression via order selection criteria. The Annals of Statistics,20:1412-1425.
79. Fan, J. and Gijbels, I. (1996). Local Polynomial Modelling and its Applications. Chapman & Hall, London.
80. Fan, J. and Li, R. (2002). Variable selection for Cox’s proportional hazards model and frailty model. Annals of Statistics,30:74-99.
81. Fenstad, A. M. (1992). How Much Dependence Can the Independence Assumption Tolerate?Cand. Scient. thesis, University of Oslo, Department of Mathematics. In Norwegian.
82. Firth, D. (1993). Bias reduction of maximum likelihood estimates. Biometrika,80:27-38.
83. Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival Analysis. John Wiley & Sons Inc., New York.
84. Foster, D. P. and George, E. I. (1994). The risk inflation criterion for multiple regression. The Annals of Statistics,22:1947-1975.
85. Frank, I. E. and Friedman, J. H. (1993). A statistical view of some chemometric regression models. Technometrics,35:109-135. With discussion contributions and a rejoinder.
86. Geisser, S. (1975). The predictive sample reuse method with applications. Journal of The American Statistical Association,70:320-328.
87. George, E. I. (1986a). Combining minimax shrinkage estimators. Journal of the American Statistical Association,81:437-445.
88. George, E. I. (1986b). Minimax multiple shrinkage estimation. The Annals of Statistics,14:188-205.
89. Grünwald, P. (2005). A tutorial introduction to the minimum description length principle. In Griinwald, P., Myung, I. J. and Pitt, M. (editors), Advances in Minimum Description Length: Theory and Applications. MIT Press, Boston.
90. Grünwald, P. (2007). The Minimum Description Length Principle, MIT Press, Boston.
91. Gurka, M. J. (2006). Selecting the best linear mixed model under REML. The American Statistician,60:19-26.
92. Guyon, X. and Yao, J.-F. (1999). On the underfitting and overfitting sets of models chosen by order selection criteria. Journal of Multivariate Analysis,70:221-249.
93. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J. and Stahel, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions. John Wiley & Sons Inc., New York.
94. Hand, D. J., Daly, F., Lunn, A., McConway, K. J. and Ostrowski, E. (1994). A Handbook of Small Data Sets. Chapman & Hall, London.
95. Hand, D. J. and Vinciotti, V. (2003). Local versus global models for classification problems: fitting models where it matters. The American Statistician,57:124-131.
96. Hannan, E. J. and Quinn, B. G. (1979). The determination of the order of an autoregression. Journal of the Royal Statistical Society, Series B,41:190-195.
97. Hansen, B. E. (2005). Challenges for econometric model selection. Econometric Theory,21:6068.
98. Hansen, M. and Yu, B. (2001). Model selection and Minimum Description Length principle. Journal of the American Statistical Association,96:746-774.
99. Hart, J. D. (1997). Nonparametric Smoothing and Lack-of-fit Tests. Springer-Verlag, New York.
100. Hart, J. D. (2008). Frequentist-Bayes lack-of-fit tests based on Laplace approximations. Journal of Statistical Theory and Practice, to appear.
101. Hart, J. D. and Yi, S. (1998). One-sided cross-validation. Journal of the American Statistical Association,93:620-631.
102. Harville, D. A. (1997). Matrix Algebra from a Statistician’s Perspective. Springer-Verlag, New York.
103. Hastie, T. J. and Tibshirani, R. J. (1990). Generalized Additive Models. Chapman & Hall, London.
104. Hastie, T. J., Tibshirani, R. J. and Friedman, J. (2001). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer-Verlag, Heidelberg.
105. Haughton, D. (1988). On the choice of a model to fit data from an exponential family. The Annals of Statistics,16:342-355.
106. Haughton, D. (1989). Size of the error in the choice of a model to fit data from an exponential family. Sankhya, Series A,51:45-58.
107. Helland, I. S. (1990). Partial least squares regression and statistical models. Scandinavian Journal of Statistics,17:97-114.
108. Henriksen, T. (2007). Ernsring, vekt og svangerskap (nutrition, weight andpregnacny). Tidsskrift for den Norske Lwgeforening,127:2399-2401.
109. Hens, N., Aerts, M. and Molenberghs, G. (2006). Model selection for incomplete and design-based samples. Statistics in Medicine,25:2502-2520.
110. Hjort, N. L. (1986a). Bayes estimators and asymptotic efficiency in parametric counting process models. Scandinavian Journal of Statistics,13:63-85.
111. Hjort, N. L. (1986b). Statistical Symbol Recognition. Research Monograph. Norwegian Computing Centre, Oslo.
112. Hjort, N. L. (1990). Nonparametric Bayes estimators based on Beta processes in models for life history data. The Annals of Statistics,18:1259-1294.
113. Hjort, N. L. (1991). Estimation in moderately misspecified models. Statistical research report, Department of Mathematics, University of Oslo.
114. Hjort, N. L. (1992a). On inference in parametric survival data models. International Statistical Review,40:355-387.
115. Hjort, N. L. (1992b). Semiparametric estimation of parametric hazard rates. In Survival Analysis: State of the Art (Columbus, OH, 1991), Vol. 211 of NATO Advanced Science Institute, Series E, Applied Science, pages 211-236. Kluwer Academic Publishers, Dordrecht. With a discussion by Mike West and Sue Leurgans.
116. Hjort, N. L. (1994a). The exact amount of t-ness that the normal model can tolerate. Journal of the American Statistical Association,89:665-675.
117. Hjort, N. L. (1994b). Minimum L2 and robust Kullback-Leibler estimation. In Proceedings of the 12th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, pages 102-105, Prague.
118. Hjort, N. L. (2007a). And Quiet does not Flow the Don: Statistical analysis of a quarrel between two Nobel Prize winners. In Østreng, W. (editor), Consilience: Interdisciplinary Communications, pages 134-140. Centre of Advanced Studies at the Norwegian Academy of Science and Letters, Oslo.
119. Hjort, N. L. (2007b). Focussed information criteria for the linear hazard rate regression model. In Vonta, F., Nikulin, M., Limnios, N. and Huber-Carol, C. (editors), Statistical Models and Methods for Biomedical and Technical Systems, Statistics for Industry and Technology, pages 491-506. IMS, Birkhauser.
120. Hjort, N. L. (2007c). A Lévy process approach to beer froth watching. Statistical research report, Department of Mathematics, University of Oslo.
121. Hjort, N. L. and Claeskens, G. (2003a). Frequentist model average estimators. Journal of the American Statistical Association,98:879-899. With discussion and a rejoinder by the authors.
122. Hjort, N. L. and Claeskens, G. (2003b). Rejoinder to the discussion of ‘frequentist model average estimators’ and ‘the focused information criterion’. Journal of the American Statistical Association,98:938-945.
123. Hjort, N. L. and Claeskens, G. (2006). Focussed information criteria and model averaging for Cox’s hazard regression model. Journal of the American Statistical Association,101:1449-1464.
124. Hjort, N. L., Dahl, F. and Steinbakk, G. (2006). Post-processing posterior predictive p-values. Journal of the American Statistical Association,101:1157-1174.
125. Hjort, N. L. and Glad, I. (1995). Nonparametric density estimation with a parametric start. The Annals of Statistics,23:882-904.
126. Hjort, N. L. and Jones, M. C. (1996). Locally parametric nonparametric density estimation. The Annals of Statistics,24:1619-1647.
127. Hjort, N. L. and Koning, A. J. (2002). Tests of constancy of model parameters over time. Journal of Nonparametric Statistics,14:113-132.
128. Hjort, N. L. and Pollard, D. B. (1993). Asymptotics for minimisers of convex processes. Statistical research report, Department of Mathematics, University of Oslo.
129. Hjort, N. L. and Rosa, D. (1999). Who won? Speedskating World,4:15-18.
130. Hjort, N. L. and Varin, C. (2008). ML, PL, QL for Markov chain models. Scandinavian Journal of Statistics,35:64-82.
131. Hjorth, U. (1994). Computer Intensive Statistical Methods: Validation, Model Selection and Bootstrap. Chapman & Hall, London.
132. Hoerl, A. E. and Kennard, R. W. (1970). Ridge regression: biased estimation for nonorthogonal problems. Technometrics,12:55-67.
133. Hoeting, J. A., Madigan, D., Raftery, A. E. and Volinsky, C. T. (1999). Bayesian model averaging: A tutorial. Statistical Science,14:382-417. With discussion by M. Clyde, D. Draper and E. I. George, and a rejoinder by the authors. [A version where the number of misprints has been significantly reduced is available at www.research.att.com/~volinsky/bma.html.]
134. Hosmer, D. W. and Hjort, N. L. (2002). Goodness-of-fit processes for logistic regression: simulation results. Statistics in Medicine,21:2723-2738.
135. Hosmer, D. W. and Lemeshow, S. (1999). Applied Logistic Regression. John Wiley & Sons Inc., New York.
136. Huber, P. J. (1981). Robust Statistics. John Wiley & Sons Inc., New York.
137. Hurvich, C. M., Simonoff, J. S. and Tsai, C.-L. (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. Journal of the Royal Statistical Society, Series B,60:271-293.
138. Hurvich, C. M. and Tsai, C.-L. (1989). Regression and time series model selection in small samples. Biometrika,76:297-307.
139. Hurvich, C. M. and Tsai, C.-L. (1990). The impact of model selection on inference in linear regression. The American Statistician,44:214-217.
140. Hurvich, C. M. and Tsai, C.-L. (1995a). Model selection for extended quasi-likelihood models in small samples. Biometrics,51:1077-1084.
141. Hurvich, C. M. and Tsai, C.-L. (1995b). Relative rates of convergence for efficient model selection criteria in linear regression. Biometrika,82:418-425.
142. Ibrahim, J. G., Chen, M.-H. and Lipsitz, S. R. (1999a). Monte Carlo EM for missing covariates in parametric regression models. Biometrics,55:591-596.
143. Ibrahim, J. G., Lipsitz, S. R. and Chen, M.-H. (1999b). Missing covariates in generalized linear models when the missing data mechanism is non-ignorable. Journal of the Royal Statistical Society, Series B,61(1):173-190.
144. Ing, C.-K. and Wei, C.-Z. (2005). Order selection for same-realization predictions in autoregressive processes. The Annals of Statistics,33:2423-2474.
145. Inglot, T., Kallenberg, W. C. M. and Ledwina, T. (1997). Data driven smooth tests for composite hypotheses. The Annals of Statistics,25:1222-1250.
146. Inglot, T. and Ledwina, T. (1996). Asymptotic optimality of data-driven Neyman’s tests for uniformity. The Annals of Statistics,24:1982-2019.
147. Jansen, M. (2001). Noise Reduction by Wavelet Thresholding, Vol. 161 of Lecture Notes in Statistics. Springer-Verlag, New York.
148. Jansen, M. and Bultheel, A. (2001). Asymptotic behavior of the minimum mean squared error threshold for noisy wavelet coefficients of piecewise smooth signals. IEEE Transactions on Signal Processing,49:1113-1118.
149. Jansen, M., Malfait, M. and Bultheel, A. (1997). Generalized cross validation for wavelet thresholding. Signal Processing,56:33-44.
150. Jeffreys, H. (1961). Theory of Probability (3rd edition). Clarendon Press, Oxford.
151. Jiang, J. (2007). Linear and Generalized Linear Mixed Models and their Applications. Springer Series in Statistics. Springer-Verlag, New York.
152. Jiang, J. and Rao, J. S. (2003). Consistent procedures for mixed linear model selection. Sankhya, 65:23-42.
153. Jiang, J., Rao, J. S., Gu, Z. and Nguyen, T. (2008). Fence methods for mixed model selection. The Annals of Statistics, 36, to appear.
154. Johnstone, I. M. and Silverman, B. W. (2004). Needles and straw in haystacks: empirical Bayes estimates of possibly sparse sequences. The Annals of Statistics,32:1594-1649.
155. Johnstone, I. M. and Silverman, B. W. (2005). Empirical Bayes selection of wavelet thresholds. The Annals of Statistics,33:1700-1752.
156. Jones, M. C., Hjort, N. L., Harris, I. R. and Basu, A. (2001). A comparison of related density-based minimum divergence estimators. Biometrika,88:865-873.
157. Kabaila, P. (1995). The effect of model selection on confidence regions and prediction regions. Econometric Theory,11:537-549.
158. Kabaila, P. (1998). Valid confidence intervals in regression after variable selection. Econometric Theory, 14:463-482.
159. Kabaila, P. and Leeb, H. (2006). On the large-sample minimal coverage probability of confidence intervals after model selection. Journal of the American Statistical Association,101:619629.
160. Kalbfleisch, J. D. and Prentice, R. L. (2002). The Statistical Analysis of Failure Time Data (2nd edition). John Wiley & Sons Inc., New York.
161. Karesen, K. (1992). Parametric Estimation: Choosing Between Narrow and Wide Models. Cand. Scient. thesis, University of Oslo, Department of Mathematics.
162. Kass, R. E. and Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90:773-795.
163. Kass, R. E. and Vaidyanathan, S. K. (1992). Approximate Bayes factors and orthogonal parameters, with application to testing equality of two binomial proportions. Journal of the Royal Statistical Society, Series B,54:129-144.
164. Kass, R. E. and Wasserman, L. (1995). A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. Journal of the American Statistical Association, 90:928-934.
165. Kass, R. E. and Wasserman, L. (1996). The selection of prior distributions by formal rules. Journal of the American Statistical Association,91:1343-1370.
166. Kauermann, G. (2005). A note on smoothing parameter selection for penalized spline smoothing. Journal of Statistical Planning and Inference,127:53-69.
167. Kjetsaa, G., Gustavsson, S., Beckman, B. and Gil, S. (1984). The Authorship of The Quiet Don. Solum/Humanities Press, Oslo.
168. Kolmogorov, A. N. (1965). Three approaches to the definition of the concept ‘quantity of information’. Problemy Peredatsi Informatsii,1(vyp. 1):3-11.
169. Konishi, S. and Kitagawa, G. (1996). Generalised information criteria in model selection. Biometrika, 83:875-890.
170. Lahiri, P. (2001). Model Selection. Institute of Mathematical Statistics Lecture Notes - Monograph Series, 38. Institute of Mathematical Statistics.
171. Le Cam, L. (1953). On some asymptotic properties of maximum likelihood estimates and related Bayes’ estimates. University of California Publications in Statistics,1:277-330.
172. Le Cam, L. and Yang, G. L. (2000). Asymptotics in Statistics: Some Basic Concepts (2nd edition). Springer-Verlag, New York.
173. le Cessie, S. and van Houwelingen, J. C. (1991). A goodness-of-fit test for binary regression models, based on smoothing methods. Biometrics,47:1267-1282.
174. le Cessie, S. and van Houwelingen, J. C. (1993). Building logistic models by means of a non parametric goodness of fit test: a case study. Statistica Neerlandica,47:97-109.
175. Ledwina, T. (1994). Data-driven version of Neyman’s smooth test of fit. Journal of the American Statistical Association,89:1000-1005.
176. Lee, M.-L. T. and Whitmore, G. A. (2007). Threshold regression for survival analysis: modeling event times by a stochastic process reaching a boundary. Statistical Science,21(4):501-513.
177. Lee, S. and Karagrigoriou, A. (2001). An asymptotically optimal selection of the order of a linear process. Sankhyā Series A,63:93-106.
178. Leeb, H. and Pötscher, B. M. (2005). Model selection and inference: facts and fiction. Econometric Theory,21:21-59.
179. Leeb, H. and Pötscher, B. M. (2006). Can one estimate the conditional distribution of post-model- selection estimators? The Annals of Statistics,34:2554-2591.
180. Leeb, H. and Pötscher, B. M. (2008). Sparse estimators and the oracle property, or the return of Hodges’ estimator. Journal of Econometrics,142:201-211.
181. Lehmann, E. L. (1983). Theory of Point Estimation. John Wiley & Sons Inc., New York.
182. Leike, A. (2002). Demonstration of the exponential decay law using beer froth. European Journal of Physics,23:21-26.
183. Li, K.-C. (1987). Asymptotic optimality for Cp, CL, cross-validation and generalized crossvalidation: discrete index set. The Annals of Statistics,15:958-975.
184. Lien, D. and Shrestha, K. (2005). Estimating the optimal hedge ratio with focus information criterion. Journal of Futures Markets,25:1011-1024.
185. Linhart, H. and Zucchini, W. (1986). Model Selection. John Wiley & Sons Inc., New York.
186. Little, R. J. A. and Rubin, D. B. (2002). Statistical Analysis with Missing Data (2nd edition). Wiley Series in Probability and Statistics. Wiley-Interscience [John Wiley & Sons], Hoboken, New Jersey.
187. Loader, C. (1996). Local likelihood density estimation. The Annals of Statistics,24:1602-1618.
188. Longford, N. T. (2005). Editorial: model selection and efficiency—is ‘which model…?’ the right question? Journal of the Royal Statistical Society, Series A,168:469-472.
189. Lu, H., Hodges, J. and Carlin, B. (2005). Measuring the complexity of generalized linear hierarchical models. Technical report, Division of Biostatistics, School of Public Health, University of Minnesota.
190. Machado, J. A. F. (1993). Robust model selection and M-estimation. Econometric Theory,9:478-493.
191. Mallows, C. L. (1973). Some comments on Cp. Technometrics,15:661-675.
192. Manly, B. F. J. (1986). Multivariate Statistical Methods. Chapman & Hall, New York.
193. Martens, H. and Nss, T. (1992). Multivariate Calibration. John Wiley & Sons Inc., New York.
194. McCullagh, P. (2002). What is a statistical model? The Annals of Statistics,30:1225-1310. With discussion and a rejoinder by the author.
195. McCullagh, P. and Nelder, J. (1989). Generalized Linear Models. Chapman & Hall, London.
196. McCulloch, C. E. and Searle, S. R. (2001). Generalized, Linear, and Mixed Models. Wiley Series in Probability and Statistics: Texts, References, and Pocketbooks Section. Wiley-Interscience [John Wiley & Sons], New York.
197. McQuarrie, A. D. R. and Tsai, C.-L. (1998). Regression and Time Series Model Selection. World Scientific Publishing Co. Inc., River Edge, New Jersey.
198. Miller, A. (2002). Subset Selection in Regression (2nd edition). Chapman & Hall/CRC, Boca Raton, Florida.
199. Morgan, B. J. T. (1992). The Analysis of Quantal Response Data. Chapman & Hall, London.
200. Muller, S. and Welsh, A. H. (2005). Outlier robust model selection in linear regression. Journal of the American Statistical Association,100:1297-1310.
201. Murata, N., Yoshizawa, S. and Amara, S. (1994). Network information criterion - determining the number of hidden units for artificial natural network models. IEEE Transactions on Neural Networks,5:865-872.
202. Murtaugh, P. A., Dickson, E. R., Vandam, G. M., Malinchoc, M., Grambsch, P. M., Langworthy, A. and Gips, C. H. (1994). Primary biliary-cirrhosis - prediction of short-term survival based on repeated patient visits. Hepatology,20:126-134.
203. Myung, J. I., Navarro, D. J. and Pitt, M. A. (2006). Model selection by normalized maximum likelihood. Journal of Mathematical Psychology,50:167-179.
204. Nason, G. P. (1996). Wavelet shrinkage using cross-validation. Journal of the Royal Statistical Society, Series B,58:463-479.
205. Neyman, J. (1937). ‘Smooth’ test for goodness of fit. SkandinaviskAktuarietidskrift,20:149-199.
206. Nishii, R. (1984). Asymptotic properties of criteria for selection of variables in multiple regression. The Annals of Statistics,12:758-765.
207. Paulsen, J. (1984). Order determination of multivariate autoregressive time series with unit roots. Journal of Time Series Analysis,5:115-127.
208. Pearson, K. (1902). On the change in expectation of life in man during a period of circa 2000 years. Biometrika,1:261-264.
209. Phillips, P. C. B. and Park, J. Y. (1988). On the formulation of Wald tests of nonlinear restrictions. Econometrica,56:1065-1083.
210. Picard, R. R. and Cook, R. D. (1984). Cross-validation of regression models. Journal of the American Statistical Association,79:575-583.
211. Pinheiro, J. and Bates, D. (2000). Mixed-Effects Models in S and S-PLUS. Springer-Verlag, New York.
212. 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.
213. Pötscher, B. M. (1989). Model selection under nonstationarity: autoregressive models and stochastic linear regression models. The Annals of Statistics,17:1257-1274.
214. Pötscher, B. M. (1991). Effects of model selection on inference. Econometric Theory,7:163-185.
215. Qian, G. (1999). Computations and analysis in robust regression model selection using stochastic complexity. Computational Statistics,14:293-314.
216. Qian, G. and Künsch, H. R. (1998). On model selection via stochastic complexity in robust linear regression. Journal of Statistical Planning and Inference,75:91-116.
217. Rao, C. R. and Wu, Y. H. (1989). A strongly consistent procedure for model selection in a regression problem. Biometrika,76:369-374.
218. Rao, J. S. and Tibsirani, R. (1997). The out-of-bootstrap method for model averaging and selection. Technical report, Department of Statistics, University of Toronto.
219. Ripley, B. D. (1996). Pattern Recognition and Neural Networks. Cambridge University Press, Cambridge.
220. Rissanen, J. (1983). A universal prior for integers and estimation by minimum description length. The Annals of Statistics,11:416-431.
221. Rissanen, J. (1987). Stochastic complexity. Journal of the Royal Statistical Society, Series B,49:223-239, 253-265. With discussion.
222. Rissanen, J. J. (1996). Fisher information and stochastic complexity. IEEE Transactions on Information Theory,42:40-47.
223. Ronchetti, E. (1985). Robust model selection in regression. Statistics & Probability Letters,3:2123.
224. Ronchetti, E. (1997). Robustness aspects of model choice. Statistica Sinica,7:327-338.
225. Ronchetti, E., Field, C. and Blanchard, W. (1997). Robust linear model selection by crossvalidation. Journal of the American Statistical Association,92:1017-1023.
226. Ronchetti, E. and Staudte, R. G. (1994). A robust version of Mallows’ CP. Journal of the American Statistical Association,89:550-559.
227. Ruggeri, F. and Vidakovic, B. (1999). A Bayesian decision theoretic approach to the choice of thresholding parameter. Statistica Sinica,9:183-197.
228. Ruppert, D., Wand, M. P. and Carroll, R. J. (2003). Semiparametric Regression. Cambridge University Press, Cambridge.
229. Saunders, C., Gammermann, A. and Vovk, V. (1998). Ridge regression learning algorithm in dual variables. In Shavlik, J. (editor), Machine Learning: Proceedings of the Fifteenth International Conference, pages 515-521.
230. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics,6:461-464.
231. Searle, S. R., Casella, G. and McCulloch, C. E. (1992). Variance Components. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. John Wiley & Sons Inc., New York.
232. Sebastiani, P. and Ramoni, M. (2001). Bayesian selection of decomposable models with incomplete data. Journal of the American Statistical Association,96(456):1375-1386.
233. Self, S. G. and Liang, K. Y. (1987). Asymptotic properties of maximum likelihood and likelihood ratio tests under nonstandard conditions. Journal of the American Statistical Association, 82:605-610.
234. Sen, P. K. and Saleh, A. K. M. E. (1987). On preliminary test and shrinkage m-estimation in linear models. The Annals of Statistics,15:1580-1592.
235. Shao, J. (1997). An asymptotic theory for linear model selection. Statistica Sinica,7:221-264. With comments and a rejoinder by the author.
236. Shao, J. (1998). Convergence rates of the generalized information criterion. Journal of Nonparametric Statistics,9:217-225.
237. Shao, J. and Tu, D. (1995). The Jackknife and Bootstrap. Springer-Verlag, New York.
238. Shen, X. and Ye, J. (2002). Adaptive model selection. Journal of the American Statistical Association,97:210-221.
239. Shepard, T. H., Mackler, B. and Finch, C. A. (1980). Reproductive studies in the iron-deficient rat. Teratology,22:329-334.
240. Shibata, R. (1976). Selection of the order of an autoregressive model by Akaike’s information criterion. Biometrika,63:117-126.
241. Shibata, R. (1980). Asymptotically efficient selection of the order of the model for estimating parameters of a linear process. The Annals of Statistics,8:147-164.
242. Shibata, R. (1981). An optimal selection of regression variables. Biometrika,68:45-54.
243. Shibata, R. (1982). Correction: ‘An optimal selection ofregression variables’. Biometrika,69:492.
244. Shibata, R. (1984). Approximate efficiency of a selection procedure for the number of regression variables. Biometrika,71:43-49.
245. Shimodaira, H. (1994). A new criterion for selecting models from partially observed data. In Cheeseman, P. and Oldford, R. W. (editors), Selecting Models from Data: Artificial Intelligence and Statistics IV, pages 21-29. Springer-Verlag, New York.
246. Silvapulle, M. J. (1994). On tests against one-sided hypotheses in some generalized linear models. Biometrics,50:853-858.
247. Silvapulle, M. J. and Silvapulle, P. (1995). A score test against one-sided alternatives. Journal of the American Statistical Association,90:342-349.
248. Simonoff, J. S. and Tsai, C.-L. (1999). Semiparametric and additive model selection using an improved Akaike information criterion. Journal of Computational and Graphical Statistics, 8:22-40.
249. Sin, C.-Y. and White, H. (1996). Information criteria for selecting possibly misspecified parametric models. Journal of Econometrics,71:207-225.
250. Smola, A. and Scholkopf, B. (1998). On a kernel-based method for pattern recognition, regression, approximation and operator inversion. Algorithmica,22:211-231.
251. Solomonoff, R. J. (1964a). A formal theory of inductive inference. I. Information and Control, 7:1-22.
252. Solomonoff, R. J. (1964b). A formal theory of inductive inference. II. Information and Control, 7:224-254.
253. Solzhenitsyn, A. I. (1974). Nevyrvannaya tajna (the not yet uprooted secret). In Stremya ‘Tihogo Dona’ (Zagadki romana), pages 1-9. YMCA-Press, Paris.
254. Spiegelberg, W. (1901). Aegyptische und Griechische Eigennamen aus Mumientiketten der Romischen Kaiserzeit. Cairo.
255. Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B,64:583-639. With a discussion and a rejoinder by the authors.
256. Spitzer, F. (1956). A combinatorial lemma and its applications to probability theory. Transactions of the American Mathematical Society,82:323-339.
257. Stein, C. (1981). Estimation of the mean of a multivariate normal distribution. The Annals of Statistics,9:1135-1151.
258. Stone, M. (1974). Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society, Series B,36:111-147. With a discussion and a rejoinder by the authors.
259. Stone, M. (1977). An asymptotic equivalence of choice of model by cross-validation and Akaike’s criterion. Journal of the Royal Statistical Society, Series B,39:44-47.
260. Stone, M. (1978). Cross-validation: a review. Math. Opeartionsforsch. Ser. Statist.,9:127-139.
261. Sugiura, N. (1978). Further analysis of the data by Akaike’s information criterion and the finite sample corrections. Communications in Statistics. Theory and Methods,7:13-26.
262. Takeuchi, K. (1976). Distribution of informational statistics and a criterion of model fitting. Suri- Kagaku (Mathematical Sciences),153:12-18. In Japanese.
263. Thomson, A. and Randall-Maciver, R. (1905). Ancient Races of the Thebaid. Oxford University Press, Oxford.
264. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B,58:267-288.
265. Tibshirani, R. (1997). The lasso method for variable selection in the Cox model. Statistics in Medicine,16:385-395.
266. Tsay, R. S. (1984). Order selection in nonstationary autoregressive models. The Annals of Statistics,12:1425-1433.
267. Uchida, M. and Yoshida, N. (2001). Information criteria in model selection for mixing processes. Statistical Inference for Stochastic Processes,4:73-98.
268. Vaida, F. and Blanchard, S. (2005). Conditional Akaike information for mixed-effects models. Biometrika,92:351-370.
269. van de Geer, S. (2008). High-dimensional generalized linear models and the lasso. Annals of Statistics,35: in press.
270. van de Geer, S. and van Houwelingen, J. C. (2008). High-dimensional data: p>n in mathematical statistics and biomedical applications. Bernoulli,10:939-942.
271. van der Linde, A. (2004). On the association between a random parameter and an observable. Test,13:85-111.
272. van der Linde, A. (2005). DIC in variable selection. Statistica Neerlandica, 59:45-56.
273. van der Vaart, A. W. (1998). Asymptotic Statistics. Cambridge University Press, Cambridge.
274. Verbeke, G. and Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. Springer Series in Statistics. Springer-Verlag, New York.
275. Verloove, S. P. and Verwey, R. Y. (1983). Project on preterm and small-for-gestational age infants in the Netherlands. PhD thesis, University of Leiden.
276. Vidakovic, B. (1998). Nonlinear wavelet shrinkage with Bayes rules and Bayes factors. Journal of the American Statistical Association,93:173-179.
277. Voldner, N., Fr0slie, K. F., B0, K., Haakstad, L. H., Hoff, C. M., Godang, K., Bollerslev, J. and Henriksen, T. (2008). Modifiable determinants of fetal macrosmia: Role of life style related factors. Acta Obstetricia et Gynecologica Scandica, to appear.
278. Volinsky, C., Madigan, D., Raftery, A. E. and Kronmal, R. A. (1997). Bayesian model averaging in proportional hazard models: predicting the risk of a stroke. Applied Statistics, 46:443-448.
279. Vonesh, E. F. and Chinchilli, V. M. (1997). Linear and Nonlinear Models for the Analysis of Repeated Measurements, Vol. 154 of Statistics: Textbooks and Monographs. Marcel Dekker Inc., New York.
280. Vu, H. T. V. and Zhou, S. (1997). Generalization of likelihood ratio tests under nonstandard conditions. The Annals of Statistics,25:897-916.
281. Vuong, Q. H. (1989). Likelihood ratio tests for model selection and nonnested hypotheses. Econo- metrica,57:307-333.
282. Wand, M. P. and Jones, M. C. (1995). Kernel Smoothing, Vol. 60 of Monographs on Statistics and Applied Probability. Chapman & Hall, London.
283. Wasserman, L. (2000). Bayesian model selection and model averaging. Journal of Mathematical Psychology,44:92-107.
284. Wei, C.-Z. (1992). On predictive least squares principles. The Annals of Statistics,20:1-42.
285. Weisberg, S. (2005). Applied Linear Regression (3rd edition). John Wiley & Sons Inc., Hoboken, New Jersey.
286. White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrica,50:125.
287. White, H. (1994). Estimation, Inference and Specification Analysis. Cambridge University Press, Cambridge.
288. Windham, M. P. (1995). Robustifying model fitting. Journal of the Royal Statistical Society, Series B, 57:599-609.
289. Woodroofe, M. (1982). On model selection and the arc sine laws. The Annals of Statistics, 10:1182-1194.
290. Yang, Y. (2001). Adaptive regression by mixing. Journal of the American Statistical Association, 96:574-588.
291. Yang, Y. (2005). Can the strengths of AIC and BIC be shared? Biometrika,92:937-950.
292. Zhang, P. (1993). On the convergence rate of model selection criteria. Communications in Statistics. Theory and Methods,22:2765-2775.
293. Zhao, L. C., Dorea, C. C. Y. and Goncalves, C. R. (2001). On determination of the order of a Markov chain. Statistical Inference for Stochastic Processes,4:273-282.
294. Zou, H. and Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society, Series B,67:301-320.