Adaptive estimation in pattern recognition by combining different procedures

Statistica Sinica

Volumn 10, Issue 4, 2000, Pages 1069-1089

  Yang, Yuhong ^a  

^a Department of Statistics Center for Statistics and Applications in Forensic Evidence Iowa State University 2438 Osborn Dr Ames   (United States)

Author keywords

Adaptive estimation; Conditional probability; Logistic regression; Minimax rate adaptation; Nonparametric classification

Indexed keywords

EID: 0347607206     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. Akaike, H. (1973). 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.
2. Barron, A. R. (1987). Are Bayes rules consistent in information? In Open Problems in Communication and Computation (edited by T. M. Cover and B. Gopinath), 85-91. Springer-Verlag, New York.
3. Barron, A. R. (1993). Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inform. Theory 39, 930-945.
4. Barron, A. R. (1994). Approximation and estimation bounds for artificial neural networks. Machine Learning 14, 115-133.
5. Barron, A. R. and Barron, R. L. (1988). Statistical learning networks: a unifying view. In Computer Science and Statistics: Proceeding of the 21st Interface, 192-203. Alexandria, Virginia.
6. Barron, A. R., Birgé, L. and Massart, P. (1999). Risk bounds for model selection via penalization. Probab. Theory Related Fields 113, 301-413.
7. Barron, A. R. and Cover, T. M. (1991). Minimum complexity density estimation. IEEE Trans. Inform. Theory 37, 1034-1054.
8. Breiman, L., Friedman, J. H., Olshen, R. and Stone, C. J. (1984). Classification and Regression Trees. Wadsworth, Belmont, CA.
9. Buja, A., Hastie, T. and Tibshirani, R. (1989). Linear smoothing and additive models. Ann. Statist. 17, 453-555.
10. Cesa-Bianchi, N., Freund, Y., Haussler, D. P., Schapire, R. and Warmuth, M. K. (1997). How to use expert advise? J. ACM 44, 427-485.
11. Cesa-Bianchi, N. and Lugosi, G. (1999). On prediction of individual sequences. To appear in Ann. Statist..
12. Clarke, B. and Barron, A. R. (1990). Information-theoretic asymptotics of Bayes methods. IEEE Trans. Inform. Theory 36, 453-471.
13. Devroye, L. (1988). Automatic pattern recognition: a study of the probability of error. IEEE Trans. Pattern Analysis and Machine Intelligence 10, 530-543.
14. 1 error of partitioning estimates of a regression functions. In Proceedings of the Fourth Pannonian Symposium on Mathematical Statistics (edited by F. Konecny, J. Mogyor ódi and W. Wertz), 67-76. Akadémiai Kiadó, Budapest, Hungary.
15. Devroye, L., Györfi, L. and Lugosi, G. (1996). A Probabilistic Theory of Pattern Recognition. Springer-Verlag, New York.
16. Friedman, J. and Stuetzel, W. (1981). Projection pursuit regression. J. Amer. Statist. Assoc. 76, 817-823.
17. Gorden, L. and Olshen, L. (1984). Almost surely consistent nonparametric regression from recursive partitioning schemes. J. Multivariate Anal. 15, 147-163.
18. Hall, P. and Hannan, E. J. (1988). On stochastic complexity and nonparametric density estimation. Biometrika 75, 705-714.
19. Littlestone, N. and Warmuth, M. K. (1994). The weighted majority algorithm. Inform. Comput. 108, 212-261.
20. Lugosi, G. and Nobel, A. (1999). Adaptive model selection using empirical complexities. Ann. Statist. 27, 1830-1864.
21. McCaffrey, D. F. and Gallant, A. R. (1994). Convergence rates for single hidden layer feedforward networks. Neural Networks 7, 147-158.
22. Nicoleris, T. and Yatracos, Y. G. (1997). Rate of convergence of estimates, Kolmogrov's entropy and the dimensionality reduction principle in regression. Ann. Statist. 25, 2493-2511.
23. Nobel, A. (1996). Histogram regression estimation using data-dependent partitions. Ann. Statist. 24, 1084-1105.
24. Rissanen, J., Speed, T. P. and Yu, B. (1992). Density estimation by stochastic complexity. IEEE Trans. Inform. Theory 38, 315-323.
25. Schwartz, G. (1978). Estimating the dimension of a model. Ann. Statist. 6, 461-464.
26. Stone, C. J. (1985). Additive regression and other nonparametric models. Ann. Statist. 13, 689-705.
27. Stone, C. J. (1994). The use of polynomial splines and their tensor products in multivariate function estimation. Ann. Statist. 22, 118-184.
28. Stone, C. J., Hansen, M. H., Kooperberg, C. and Truong, Y. (1997). Polynomial splines and their tensor products in extended linear modeling (with discussion). Ann. Statist. 25, 1371-1470.
29. Stone, M. (1974). Cross-validatory choice and assessment of statistical predictions (with discussion). J. Roy. Statist. Soc. Ser. B 36, 111-147.
30. Vovk, V. G. (1990). Aggregating strategies. In Proceedings of the 3rd Annual Workshop on Computational Learning Theory, 372-383.
31. Yang, Y. (1996). Minimax Optimal Density Estimation. Ph.D. Dissertation, Department of Statistics, Yale University.
32. Yang, Y. (1999a). Model selection for nonparametric regression. Statist. Sinica 9, 475-499.
33. Yang, Y. (1999b). Minimax nonparametric classification - part I: rates of convergence. IEEE Trans. Inform. Theory 45, 2271-2284.
34. Yang, Y. (1999c). Minimax nonparametric classification - part II: model selection for adaptation. IEEE Trans. Inform. Theory 45, 2285-2291.
35. Yang, Y. (1999d). Regression with multiple candidate models: selecting or mixing? Technical Report #8, Department of Statistics, Iowa State University.
36. Yang, Y. (2000a). Combining different procedures for adaptive regression. J. Multivariate Anal. 74, 135-161.
37. Yang, Y. (2000b). Mixing strategies for density estimation. Ann. Statist. 28, 75-87.
38. Yang, Y. and Barron, A. R. (1998). An asymptotic property of model selection criteria. IEEE Trans. Inform. Theory 44, 95-116.
39. Yang, Y. and Barron, A. R. (1999). Information-theoretic determination of minimax rates of convergence. Ann. Statist. 27, 1564-1599.