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
Recommended Citation
Brown, L. D., & Levine, M. (2007). Variance Estimation in Nonparametric Regression via the Difference Sequence Method. The Annals of Statistics, 35 (5), 2219-2232. http://dx.doi.org/10.1214/009053607000000145
Date Posted: 27 November 2017
This document has been peer reviewed.