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September, 1984 Asymptotic Normality of Nearest Neighbor Regression Function Estimates
Winfried Stute
Ann. Statist. 12(3): 917-926 (September, 1984). DOI: 10.1214/aos/1176346711

Abstract

Let $(X, Y)$ be a random vector in the plane. We show that a smoothed N.N. estimate of the regression function $m(x) = \mathbb{E}(Y\mid X = x)$ is asymptotically normal under conditions much weaker than needed for the Nadaraya-Watson estimate. It also turns out that N.N. estimates are more efficient than kernel-type estimates if (in the mean) there are few observations in neighborhoods of $x$.

Citation

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Winfried Stute. "Asymptotic Normality of Nearest Neighbor Regression Function Estimates." Ann. Statist. 12 (3) 917 - 926, September, 1984. https://doi.org/10.1214/aos/1176346711

Information

Published: September, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0539.62026
MathSciNet: MR751282
Digital Object Identifier: 10.1214/aos/1176346711

Subjects:
Primary: 62J02
Secondary: 62E20, 62G05

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 3 • September, 1984
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