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Pré-Publication, Document De Travail Année : 2015

Minimal penalty for Goldenshluger-Lepski method

Résumé

This paper is concerned with adaptive nonparametric estimation using the Goldenshluger-Lepski methodology. This method is designed to select an estimator among a collection $(\hat f_h)_{h\in H}$ by minimizing $B(h)+V(h)$ with $B(h)=\sup\{[\|\hat f_{h'}- \hat f_{h}\|-V(h')]_+, \: h'\in H\}$ and $V(h)$ a variance term. In the case of density estimation with kernel estimators, it is shown that the procedure fails if the variance term is chosen too small: this gives for the first time a minimal penalty for the Goldenshluger-Lepski methodology. Some simulations illustrate the theoretical results.
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Dates et versions

hal-01121989 , version 1 (03-03-2015)
hal-01121989 , version 2 (29-02-2016)

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Claire Lacour, Pascal Massart. Minimal penalty for Goldenshluger-Lepski method. 2015. ⟨hal-01121989v1⟩
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