Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression
Statistics Theory
2010-02-09 v1 Statistics Theory
Abstract
The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper, 2007, for estimating an unknown nonparametric regression. %\cite{GaPe1}. We prove that this procedure is asymptotically efficient for a quadratic risk, i.e. the asymptotic quadratic risk for this procedure coincides with the Pinsker constant which gives a sharp lower bound for the quadratic risk over all possible estimates
Cite
@article{arxiv.1002.1537,
title = {Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression},
author = {Leonid Galtchouk and Serguei Pergamenchtchikov},
journal= {arXiv preprint arXiv:1002.1537},
year = {2010}
}