Asymptotically minimax regret procedures in regression model selection and the magnitude of the dimension penalty

Annals of Statistics

Volumn 28, Issue 6, 2000, Pages 1620-1637

  Goldenshluger, Alexander ^a   Greenshtein, Eitan ^b  

^a UNIVERSITY OF HAIFA   (Israel)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Minimax procedures; Model selection; Regression

Indexed keywords

EID: 0034343424     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1015957473     Document Type: Article

References (22)

1. AKAIKE, H. (1974). A new look at the statistical identification model. IEEE Trans. Automat. Control 19 716-723.
2. BREIMAN, L. and FREEDMAN, D. (1983). How many variables should be entered in a regression equation? J. Amer. Statist. Assoc. 78 131-136.
3. FOSTER, D. P. and GEORGE, E. I. (1994). The risk inflation criterion for multiple regression. Ann. Statist. 22 1947-1975.
4. GEISSER, S. (1975). The predictive sample reuse method with applications. J. Amer. Statist. Assoc. 70 320-328.
5. GOLDENSHLUGER, A. and GREENSHTEIN, E. (1998). Asymptotic minimax procedures in regression model selection and the magnitude of the dimension penallty. Technical report, Technion-Israel Institute of Technology.
6. GREENSHTEIN, E. (2000). Predictor-selection. Another look on model-selection and estimation. Technical report, Technion-Israel Institute of Technology.
7. HANNAN, E. J. and QUINN, B. G. (1979). The determi iation of the order of an autoregression. J. Roy. Statist. Soc. Ser. B 41 190-195.
8. LINHART, H. and ZUCHINI, W. (1986). Model selection. Wiley, New York.
9. p. Technometrics 15 661-675.
10. NISHII, R. (1984). Asymptotic properties of criteria for selection of variables in multiple regression. Ann. Statist. 12 758-765.
11. OLIKER, V. I. (1978). On the relationship between the simple size and the number of variables in a linear regression model. Comm. Statist. A 7 509-516.
12. RISSANEN, J. (1989). Stochastic Complexity in Statistical Inquiry. World Books, Singapore.
13. SCHWARZ, G. (1978). Estimating the dimension of a model. Ann. Statist. 6 461-464.
14. SHAO, J. (1997). An asymptotic theory for linear model selection. Statist. Sinica 7 221-264.
15. SHIBATA, R. (1981). An optimal selection of regression variables. Biometrika 68 45-54.
16. SHIBATA, R. (1986). Selection of the number of regression variables: a minimax choice of generalized FPE. Ann. Inst. Statist. Math. 38 459-474.
17. SHIBATA, R. (1989). Statistical aspects of model selecticn. From Data to Model (J. C. Willems, ed.) 215-240. Springer, New York.
18. SPEED, T. and YU, B. (1993). Model selection and prediction: normal regression. Ann. Inst. Statist. Math. 45 35-54.
19. STONE, C. J. (1981). Admissible selection of an accurate and parsimonious normal linear regression model. Ann. Statist. 9 475-485.
20. STONE, M. (1974). Cross-validatory choice and assessment of statistical predictions. J. Royal Statist. Soc. Ser. B 36 111-147.
21. STONE, M. (1977). An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion. J. Royal Statist. Soc. Ser. B 39 44-47.
22. THOMPSON, M. L. (1978). Selection of variables in multiple regression. Internat. Statist. Rev. 46 1-49 and 129-146.