| Title:
|
Strong consistency of regression function estimates (English) |
| Author:
|
Lin, Zhang Shuang |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
31 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
375-384 |
| . |
| Category:
|
math |
| . |
| MSC:
|
62G05 |
| MSC:
|
62G07 |
| MSC:
|
62G20 |
| MSC:
|
62J02 |
| idZBL:
|
Zbl 0857.62041 |
| idMR:
|
MR1357351 |
| . |
| Date available:
|
2009-09-24T18:56:40Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124674 |
| . |
| Reference:
|
[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. |
| Reference:
|
[2] G. Collomb: Nonparametric regression: an up-to-date bibliography.Statistics 16 (1985), 300-324. Zbl 0574.62043 |
| Reference:
|
[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 0057518 |
| Reference:
|
[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 0682574 |
| Reference:
|
[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 0851019 |
| Reference:
|
[6] L. Devroye L. Gyorfi G. Lugosi, A. Krzyzak: On strong universal consistency of nearest neighbor regression function estimates.Ann. Statist. To appear. MR 1311980 |
| Reference:
|
[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 1029241 |
| Reference:
|
[8] L. Devroye, T.J. Wagner: Distribution-free consistency results in nonparametric discrimination and regression function estimation.Ann. Statist. 8 (1980), 231-239. Zbl 0431.62025, MR 0560725 |
| Reference:
|
[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. Zbl 0795.62035, MR 1244063 |
| Reference:
|
[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 1154338 |
| Reference:
|
[11] E. A. Nadaraya: On estimating regression.Theory Probab. Appl. 5 (1964), 141-142. Zbl 0136.40902 |
| Reference:
|
[12] C. Spiegelman, J. Sacks: Consistent window estimation in nonparametric regression.Ann. Statist. 8 (1980), 240-246. Zbl 0432.62066, MR 0560726 |
| Reference:
|
[13] C. J. Stone: Consistent nonparametric regression.Ann. Statist. 8 (1977), 1348-1360. Zbl 0366.62051, MR 0594650 |
| Reference:
|
[14] G. S. Watson: Smooth regression analysis.Sankhya. Ser. A 26 (1964), 359-372. Zbl 0137.13002, MR 0185765 |
| Reference:
|
[15] L. C. Zhao: Exponential bounds of mean error for the nearest neighbor estimates of regression functions.J. Multivariate Anal. 21 (1987), 168-178. Zbl 0622.62044, MR 0877849 |
| . |
