Strong consistency of regression function estimates
Kybernetika, Tome 31 (1995) no. 4, pp. 375-384 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 62G05, 62G07, 62G20, 62J02
@article{KYB_1995_31_4_a5,
     author = {Lin, Zhang Shuang},
     title = {Strong consistency of regression function estimates},
     journal = {Kybernetika},
     pages = {375--384},
     year = {1995},
     volume = {31},
     number = {4},
     mrnumber = {1357351},
     zbl = {0857.62041},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1995_31_4_a5/}
}
TY  - JOUR
AU  - Lin, Zhang Shuang
TI  - Strong consistency of regression function estimates
JO  - Kybernetika
PY  - 1995
SP  - 375
EP  - 384
VL  - 31
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/KYB_1995_31_4_a5/
LA  - en
ID  - KYB_1995_31_4_a5
ER  - 
%0 Journal Article
%A Lin, Zhang Shuang
%T Strong consistency of regression function estimates
%J Kybernetika
%D 1995
%P 375-384
%V 31
%N 4
%U http://geodesic.mathdoc.fr/item/KYB_1995_31_4_a5/
%G en
%F KYB_1995_31_4_a5
Lin, Zhang Shuang. Strong consistency of regression function estimates. Kybernetika, Tome 31 (1995) no. 4, pp. 375-384. http://geodesic.mathdoc.fr/item/KYB_1995_31_4_a5/

[1] J. Beck: The exponential rate of convergence of error for $k_n$ NN nonparametric regression and decision. Problems Control Inform. Theory 8 (1979), 303-311.

[2] G. Collomb: Nonparametric regression: an up-to-date bibliography. Statistics 16 (1985), 300-324. | Zbl

[3] H. Chernoff: A measure of asymptotic efficiency of tests of a hypothesis based on the sum of observations. Ann. Math. Statist. 25 (1952), 493-507. | MR

[4] L. Devroye: Necessary and sufficient conditions for the almost everywhere convergence of nearest neighbor regression function estimates. Z. Wahrsch. verw. Geb. 61 (1982), 467-481. | MR

[5] L. Devroye, L. Gyorfi: Distribution-free exponential bound on the $L_1$ error of partitioning estimates of a regression function. In: Proceedings of the Fourth Pannonian Symposium on Mathematical Statistics (F. Konecny, J. Mogyorodi, W. Wertz, eds.), Akademiai Kiado, Budapest 1983, pp. 67-76. | MR

[6] L. Devroye L. Gyorfi G. Lugosi, A. Krzyzak: On strong universal consistency of nearest neighbor regression function estimates. Ann. Statist. To appear. | MR

[7] L. Devroye, A. Krzyzak: An equivalence theorem for $L_1$ convergence of the kernel regression estimate. J. Statist. Plann. Inference 23 (1989), 71-82. | MR

[8] L. Devroye, T.J. Wagner: Distribution-free consistency results in nonparametric discrimination and regression function estimation. Ann. Statist. 8 (1980), 231-239. | MR | Zbl

[9] M. Falk, R. D. Reiss: A Hellinger distance bound for the nearest neighbor approach in conditional curve estimation. Statist. Decisions, Supplement Issue 3 (1993), 55-68. | MR | Zbl

[10] L. Gyorfi: Universal consistencies of a regression estimate for unbounded regression functions. In: Nonparametric Functional Estimation (G. Roussas, ed.), NATO ASI Series, Springer-Verlag, Berlin 1991, pp. 329-338. | MR

[11] E. A. Nadaraya: On estimating regression. Theory Probab. Appl. 5 (1964), 141-142. | Zbl

[12] C. Spiegelman, J. Sacks: Consistent window estimation in nonparametric regression. Ann. Statist. 8 (1980), 240-246. | MR | Zbl

[13] C. J. Stone: Consistent nonparametric regression. Ann. Statist. 8 (1977), 1348-1360. | MR | Zbl

[14] G. S. Watson: Smooth regression analysis. Sankhya. Ser. A 26 (1964), 359-372. | MR | Zbl

[15] L. C. Zhao: Exponential bounds of mean error for the nearest neighbor estimates of regression functions. J. Multivariate Anal. 21 (1987), 168-178. | MR | Zbl