An application of multiple comparison techniques to model selection

Annals of the Institute of Statistical Mathematics

Volumn 50, Issue 1, 1998, Pages 1-13

  Shimodaira, Hidetoshi ^a,b  

^a UNIVERSITY OF TOKYO   (Japan)

^b INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

Author keywords

Akaike's information criterion; Bootstrap resampling; Confidence set; Gupta's subset selection; Model selection; Multiple comparison with the best; Multiple regression; Variable selection

Indexed keywords

EID: 7744247581     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1003483128844     Document Type: Article

References (26)

1. Aitkin, M. A. (1974). Simultaneous inference and the choice of variable subsets in multiple regression, Technometrics, 16, 221-227.
2. Akaike, H. (1974). A new look at the statistical model identification, IEEE Trans Automat Control, 19, 716-723.
3. Akaike, H. (1979). A Bayesian extension of the minimum AIC procedure of autoregressive model fitting, Biometrika, 66, 237-242.
4. Arvesen, J. N. and McCabe, G. P., Jr. (1975). Subset selection problems for variances with applications to regression analysis, J. Amer. Statist. Assoc., 70, 166-170.
5. Atkinson, A. C. (1970). A method for discriminating between models, J. Roy. Statist. Soc. Ser. B, 32, 323-353.
6. Belsley, D. A., Kuh, E. and Welsch, R. E. (1980). Regression Diagnostics, Wiley, New York.
7. Bozdogan, H. (1987). Model selection and Akaike's information criterion (AIC): the general theory and its analytical extensions, Psychometrika, 52, 345-370.
8. Cox, D. R. (1962). Further results on tests of separate families of hypotheses, J. Roy. Statist. Soc. Ser. B, 24, 406-424.
9. Dastoor, N. K. and McAleer, M. (1989). Some power comparisons of joint and paired tests for nonnested models under local hypotheses, Econometric Theory, 5, 83-94.
10. Draper, N. and Smith, H. (1981). Applied Regression Analysis (2nd ed.), Wiley, New York.
11. Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap, Chapman & Hall, New York.
12. Efron, B., Halloran, E. and Holmes, S. (1996). Bootstrap confidence levels for phylogenetic trees, Proc. Nat. Acad. Sci. U.S.A., 93, 13429-13434.
13. Felsenstein, J. (1985). Confidence limits on phylogenies: an approach using the bootstrap, Evolution, 39, 783-791.
14. Felsenstein, J. and Kishino, H. (1993). Is there something wrong with the bootstrap on phylogenies? A reply to Hillis and Bull, Systematic Biology, 42, 193-200.
15. Gupta, S. S. and Huang, D. Y. (1976). Selection procedures for the means and variances of normal populations: unequal sample sizes case, Sankhyā Ser. B, 38, 112-128.
16. Gupta, S. S. and Panchapakesan, S. (1979). Multiple Decision Procedures, Wiley, New York.
17. Hochberg, Y. and Tamhane, A. C. (1987). Multiple Comparison Procedures, Wiley, New York.
18. Linhart, H. (1988). A test whether two AIC's differ significantly, South African Statistical Journal, 22, 153-161.
19. p, Technometrics, 15, 661-675.
20. Shimodaira, H. (1993). A model search technique based on confidence set and map of models, Proc. Inst. Statist. Math., 41, 131-147 (in Japanese).
21. Shimodaira, H. (1997a). Assessing the error probability of the model selection test, Ann. Inst. Statist. Math., 49, 395-410.
22. Shimodaira, H. (1997b). A graphical technique for finding a set of good models using AIC and its variance, Ann. Inst. Statist. Math. (submitted).
23. Spjøtvoll, E. (1972). Multiple comparison of regression functions, The Annals of Mathematical Statistics, 43, 1076-1088.
24. p in multiple regression, Biometrika, 64, 1-8.
25. Vuong, Q. H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses, Econometrica, 57, 307-333.
26. White, H. (1982). Maximum likelihood estimation of misspecified models, Econometrica, 50, 1-25.