Structural adaptation via $L_p$-norm oracle inequalities
Statistics Theory
2007-05-23 v1 Probability
Statistics Theory
Abstract
In this paper we study the problem of adaptive estimation of a multivariate function satisfying some structural assumption. We propose a novel estimation procedure that adapts simultaneously to unknown structure and smoothness of the underlying function. The problem of structural adaptation is stated as the problem of selection from a given collection of estimators. We develop a general selection rule and establish for it global oracle inequalities under arbitrary --losses. These results are applied for adaptive estimation in the additive multi--index model.
Cite
@article{arxiv.0704.2492,
title = {Structural adaptation via $L_p$-norm oracle inequalities},
author = {A. Goldenhsluger and O. Lepski},
journal= {arXiv preprint arXiv:0704.2492},
year = {2007}
}