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September, 1994 On the Strong Universal Consistency of Nearest Neighbor Regression Function Estimates
Luc Devroye, Laszlo Gyorfi, Adam Krzyzak, Gabor Lugosi
Ann. Statist. 22(3): 1371-1385 (September, 1994). DOI: 10.1214/aos/1176325633

Abstract

Two results are presented concerning the consistency of the $k$-nearest neighbor regression estimate. We show that all modes of convergence in $L_1$ (in probability, almost sure, complete) are equivalent if the regression variable is bounded. Under the additional conditional $k/\log n \rightarrow \infty$ we also obtain the strong universal consistency of the estimate.

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Luc Devroye. Laszlo Gyorfi. Adam Krzyzak. Gabor Lugosi. "On the Strong Universal Consistency of Nearest Neighbor Regression Function Estimates." Ann. Statist. 22 (3) 1371 - 1385, September, 1994. https://doi.org/10.1214/aos/1176325633

Information

Published: September, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0817.62038
MathSciNet: MR1311980
Digital Object Identifier: 10.1214/aos/1176325633

Subjects:
Primary: 62G05

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 3 • September, 1994
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