Structural adaptation via $L_p$-norm oracle inequalities

Details Structural adaptation via $L_p$-norm oracle inequalities Structural adaptation via $L_p$-norm oracle inequalities

2007-04-19

arxiv.org/abs/0704.2492v1

Mathematics

Statistics Theory

Scientific paper

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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