Previous |  Up |  Next

Article

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
.

Files

Files Size Format View
Kybernetika_31-1995-4_6.pdf 901.1Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo