An alternative point of view on Lepski's method

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 finitedimensional linear subspaces. It is also shown that a suitable tuning of the method allows to asymptotically recover the best possible risk in the family. AMS subject classif?cations: Primary: 62G07, Secondary 62G20.

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