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arXiv · 0704.2492

Structural adaptation via $L_p$-norm oracle inequalities

A. Goldenhsluger·O. Lepski
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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 $\rL_p$--losses. These results are applied for adaptive estimation in the additive multi--index model.

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A. Goldenhsluger, O. Lepski. 2007-04-19. Structural adaptation via $L_p$-norm oracle inequalities. https://arxiv.org/abs/0704.2492

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