Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

An alternative point of view on Lepski's method

Auteur(s):

Code(s) de Classification MSC:

Résumé: Lepski's method is a method for choosing a ``best" estimator (in an appropriate sense) among a family of those, under suitable restrictions on this family. The subject of this paper is to give a nonasymptotic presentation of Lepski's method in the context of Gaussian regression models for a collection of projection estimators on some nested family of finite-dimensional linear subspaces. It is also shown that a suitable tuning of the method allows to asymptotically recover the best possible risk in the family.

Mots Clés: Adaptation ; Lepski's method ; Mallows' $C_p$ ; optimal selection of estimators

Date: 1999-12-08

Prépublication numéro: PMA-549

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