Statistics Papers

Document Type

Journal Article

Date of this Version

2007

Publication Source

The Annals of Statistics

Volume

35

Issue

5

Start Page

2219

Last Page

2232

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.

Keywords

nonparametric regression, variance estimation, asymptotic minimaxity

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Date Posted: 27 November 2017

This document has been peer reviewed.