Date of this Version
The Annals of Statistics
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.
nonparametric regression, variance estimation, asymptotic minimaxity
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.