Model selection for nonparametric regression

Statistica Sinica

Volumn 9, Issue 2, 1999, Pages 475-499

  Yang, Yuhong ^a  

^a E005A Lagomarcino Hall   (United States)

Author keywords

Adaptive estimation; Model complexity; Model selection; Nonparametric regression; Rates of convergence

Indexed keywords

EID: 0346208510     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. Akaike, H. (1970). Statistical prediction identification. Ann. Inst. Statist. Math. 22, 203-217.
2. Akaike, H. (1972). Information theory and an extension of the maximum likelihood principle. In Proc. 2nd Int. Symp. Info. Theory (Edited by B. N. Petrov and F. Csaki), 267-281. Akademia Kiado, Budapest.
3. Barron, A. R. (1985). Logistically smooth density estimation. Ph.D. dissertation, Department of Electrical Engineering, Stanford University.
4. Barron, A. R. (1993). Universal approximation bounds for superposition of a sigmoidal function. IEEE Trans. Inform. Theory 39, 930-945.
5. Barron, A. R. (1994). Approximation and estimation bounds for artificial neural networks. Machine Learning 14, 115-133.
6. Barron, A. R. and Sheu, C.-H. (1991). Approximation of density functions by sequences of exponential families. Ann. Statist. 19, 1347-1369.
7. Barron, A. R. and Cover, T. M. (1991). Minimum complexity density estimation. IEEE Trans. Inform. Theory 37, 1034-1054.
8. Barron, A. R., Birgé, L. and Massart, P. (1997). Risk bounds for model selection via penalization. To appear in Probab. Theory Related Fields.
9. Birgé, L. and Massart, P. (1996). From model selection to adaptive estimation. In Research Papers in Probability and Statistics: Festschrift for Lucien Le Cam (Edited by D. Pollard, E. Togersen and G. Yang), 55-87. Springer, New York.
10. Brown, L. D. and Low, M. G. (1996). A constrained risk inequality with applications to non-parametric functional estimation. Ann. Statist. 24, 2524-2535.
11. Burman, P. (1990). Estimation of generalized additive models. J. Multiariate Anal. 32, 230-255.
12. Chen, Z. (1991). Interaction spline models and their convergence rates. Ann. Statist. 19, 1855-1868.
13. Cover, T. M. and Thomas, J. A. (1991). Elements of Information Theory. Wiley, New York.
14. Donoho, D. and Johnstone, I. (1998). Minimax estimation via Wavelet Shrinkage. Ann. Statist. 26, 879-921.
15. Donoho, D. L., Johnstone, I. M., Kerkyacharian, G. and Picard, D. (1996). Density estimation by wavelet thresholding. Ann. Statist. 24, 508-539.
16. Efroimovich, S. Yu. (1985). Nonparametric estimation of a density of unknown smoothness. Theory Probab. Appl. 30, 557-568.
17. Efroimovich, S. Yu. and Pinsker, M. S. (1984). A self-educating nonparametric filtration algorithm. Automat. Remote Control 45, 58-65.
18. Elias, P. (1975). Universal codeword sets and representation of integers. IEEE Trans. Inform. Theory 21, 194-203.
19. Hall, P. and Hannan, E. J. (1988). On stochastic complexity and nonparametric density estimation. Biometrika 75, 705-714.
20. Härdle, W. and Marron, J. S. (1985). Optimal bandwidth selection in nonparametric regression function estimation. Ann. Statist. 13, 1465-1481.
21. Lepskii, O. V. (1991). Asymptotically minimax adaptive estimation I: Upper bounds. Optimally adaptive estimates. Theory Probab. Appl. 36, 682-697.
22. L, cross-validation and generalized cross-validation: discrete index set. Ann. Statist. 15, 958-975.
23. Lorentz, G. G. (1966). Metric entropy and approximation. Bull. Amer. Math. Soc. 72, 903-937.
24. p. Technometrics 15, 661-675.
25. Pollard, D. (1984). Convergence of Stochastic Processes. Springer-Vorlag, New York.
26. p-test for the orthogonal series estimation of regression. Theory Probab. Appl. 35, 293-306.
27. Rissanen, J. (1983). A universal prior for integers and estimation by minimum description length. Ann. Statist. 11, 416-431.
28. Rissanen, J. (1984). Universal coding, information, prediction, and estimation. IEEE Trans. Inform. Theory 30, 629-636.
29. Rissanen, J. (1987). Stochastic complexity. J. Roy. Statist. Soc. B 49, 223-239.
30. Shibata, R. (1983). Asymptotic mean efficiency of a selection of regression variables. Ann. Inst. Statist. Math. 35, 415-423.
31. Schumaker, L. L. (1981). Spline Functions: Basic Theory. Wiley, New York.
32. Stone, C. J. (1977). Consistent nonparametric regression. Ann. Statist. 5, 595-620.
33. Stone, C. J. (1985). Additive regression and other nonparametric models. Ann. Statist. 13, 689-705.
34. Stone, C. J. (1994). The use of polynomial splines and their tensor products in multivariate function estimation. Ann. Statist. 22, 118-184.
35. Wallace, C. S. and Boulton, D. M. (1987). Estimation and inference by compact coding. J. Roy. Statist. Soc. Ser. B 49, 240-265.
36. Yang, Y. (1997). On adaptive function estimation. Submitted to Ann. Statist.
37. Yang, Y. and Barron, A. R. (1997). Information-theoretic determination of minimax rates of convergence. Submitted to Ann. Statist.
38. Yang, Y. and Barron, A. R. (1998). An asymptotic property of model selection criteria. IEEE Trans. Inform. Theory 44, 95-116.
39. Yu, B. and Speed, T. (1992). Data compression and histogram. Probab. Theory Related Fields 92, 195-229.