The Annals of Statistics

On the Strong Universal Consistency of Nearest Neighbor Regression Function Estimates

Luc Devroye, Laszlo Gyorfi, Adam Krzyzak, and Gabor Lugosi

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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.

Article information

Source
Ann. Statist., Volume 22, Number 3 (1994), 1371-1385.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325633

Digital Object Identifier
doi:10.1214/aos/1176325633

Mathematical Reviews number (MathSciNet)
MR1311980

Zentralblatt MATH identifier
0817.62038

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation

Keywords
Regression function nonparametric estimation consistency strong convergence nearest neighbor estimate

Citation

Devroye, Luc; Gyorfi, Laszlo; Krzyzak, Adam; Lugosi, Gabor. On the Strong Universal Consistency of Nearest Neighbor Regression Function Estimates. Ann. Statist. 22 (1994), no. 3, 1371--1385. doi:10.1214/aos/1176325633. https://projecteuclid.org/euclid.aos/1176325633


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