An alternative point of view on Lepski's method
Lucien Birgé · Lecture notes-monograph series · 2001
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.