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October 2007 Variance estimation in nonparametric regression via the difference sequence method
Lawrence D. Brown, M. Levine
Ann. Statist. 35(5): 2219-2232 (October 2007). DOI: 10.1214/009053607000000145

Abstract

Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized, and asymptotic normality is also established. We also show that for suitable asymptotic formulations our estimators achieve the minimax rate.

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Lawrence D. Brown. M. Levine. "Variance estimation in nonparametric regression via the difference sequence method." Ann. Statist. 35 (5) 2219 - 2232, October 2007. https://doi.org/10.1214/009053607000000145

Information

Published: October 2007
First available in Project Euclid: 7 November 2007

zbMATH: 1126.62024
MathSciNet: MR2363969
Digital Object Identifier: 10.1214/009053607000000145

Subjects:
Primary: 62G08 , 62G20

Keywords: asymptotic minimaxity , Nonparametric regression , variance estimation

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 5 • October 2007
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