Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression via model selection
Statistics Theory
2008-10-08 v1 Statistics Theory
Abstract
The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper, 2007, for estimating a unknown nonparametric regression. 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 estimators.
Cite
@article{arxiv.0810.1173,
title = {Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression via model selection},
author = {Leonid Galtchouk and Serguey Pergamenshchikov},
journal= {arXiv preprint arXiv:0810.1173},
year = {2008}
}