Model selection in nonparametric regression

Annals of Statistics

Volumn 31, Issue 1, 2003, Pages 252-273

  Wegkamp, Marten ^a  

^a YALE UNIVERSITY   (United States)

Author keywords

Adaptive estimation; Classification; Data splitting; Least squares estimation; Model selection; Penalized least squares; VC major classes

Indexed keywords

EID: 21144432799     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1046294464     Document Type: Article

References (22)

1. ANTHONY, M. and BARTLETT, P. (1999). Neural Network Learning: Theoretical Foundations. Cambridge Univ. Press.
2. BARAUD, Y. (2000). Model selection for regression on a fixed design. Probab. Theory Related Fields 117 467-493.
3. BARRON, A. (1987). Are Bayes rules consistent in information? In Open Problems in Communication and Computation (T. Cover and B. Gopinath, eds.) 85-91. Springer, Berlin.
4. BARRON, A. (1991). Complexity regularization with applications to artificial neural networks. In Nonparametric Functional Estimation and Related Topics (G. Roussas, ed.) 561-576. Kluwer, Dordrecht.
5. BARRON, A., BIRGÉ, L. and MASSART, P. (1999). Risk bounds for model selection via penalization. Probab. Theory Related Fields 113 301-413.
6. BARTLETT, P., BOUCHERON, S. and LUGOSI, G. (2002). Model selection and error estimation. Machine Learning 48 85-113.
7. DEVROYE, L. and LUGOSI, G. (1996). A universally acceptable smoothing factor for kernel density estimates. Ann. Statist. 24 2499-2512.
8. DEVROYE, L. and LUGOSI, G. (1997). Nonasymptotic universal smoothing factors, kernel complexity and Yatracos classes. Ann. Statist. 25 2626-2635.
9. EINMAHL, U. and MASON, D. (1996). Some universal results on the behavior of increments of partial sums. Ann. Probab. 24 1388-1407.
10. HENGARTNER, N., WEGKAMP, M. and MATZNER-LØBER, E. (2002). Bandwidth selection for local linear regression smoothers. J. R. Stat. Soc. Ser. B Stat. Methodol. 64 791-804.
11. HENGARTNER, N. and WEGKAMP, M. (1999). A note on model selection procedures in nonparametric classification. Preprint, Dept. Statistics, Yale Univ.
12. 1-approach. Canad. J. Statist. 29 621-632.
13. IBRAGIMOV, R. and SHARAKHMETOV, SH. (1998). On an exact constant for the Rosenthal inequality. Theory Probab. Appl. 42 294-302.
14. LUGOSI, G. and NOBEL, A. (1999). Adaptive model selection using empirical complexities. Ann. Statist. 27 1830-1864.
15. SHAO, J. (1993). Linear model selection by cross-validation. J. Amer. Statist. Assoc. 88 486-494.
16. VAN DE GEER, S. (1990). Estimating a regression function. Ann. Statist. 18 907-924.
17. VAN DE GEER, S. (2000). Applications of Empirical Process Theory. Cambridge Univ. Press.
18. VAN DE GEER, S. and WEGKAMP, M (1996). Consistency for the least squares estimator in nonparametric regression. Ann. Statist. 24 2513-2523.
19. VAPNIK, V. (1998). Statistical Learning Theory. Wiley, New York.
20. WEGKAMP, M. H. (1999). Quasi-universal bandwidth selection for kernel density estimators. Canad. J. Statist. 27 409-420
21. YANG, Y. (2001). Adaptive regression by mixing. J. Amer. Statist. Assoc. 96 574-588.
22. YANG, Y. and BARRON, A. (1999). Information-theoretic determination of minimax rates of convergence. Ann. Statist. 27 1564 - 1599.