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March, 1984 Integrated Square Error Properties of Kernel Estimators of Regression Functions
Peter Hall
Ann. Statist. 12(1): 241-260 (March, 1984). DOI: 10.1214/aos/1176346404

Abstract

Weak laws of large numbers and central limit theorems are proved for integrated square error of kernel estimators of regression functions. The regressor is assumed to take values in $\mathbb{R}^p$, and the regressand, $X$, to be real valued. It is shown that in many cases, integrated square error is asymptotically normally distributed and independent of the $X$-sample. As an application, a test for the regression function (such as that proposed by Konakov) is seen to be asymptotically independent of an arbitrary test based on the $X$-sample. The proofs involve martingale methods.

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Peter Hall. "Integrated Square Error Properties of Kernel Estimators of Regression Functions." Ann. Statist. 12 (1) 241 - 260, March, 1984. https://doi.org/10.1214/aos/1176346404

Information

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

zbMATH: 0544.62036
MathSciNet: MR733511
Digital Object Identifier: 10.1214/aos/1176346404

Subjects:
Primary: 62G20
Secondary: 60F05, 62E20

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 1 • March, 1984
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