An alternative point of view on Lepski's method

被引：63

作者：

Birgé, L ^{[1
]}

机构：

[1] Univ Paris 06, Lab Probabil & Modeles Stochast, F-75252 Paris 05, France

来源：

STATE OF THE ART IN PROBABILITY AND STATISTICS: FESTSCHRIFT FOR WILLEM R VAN ZWET | 2001年 / 36卷

关键词：

adaptation; Lepski's method; mallows' C-p; optimal selection of estimators;

D O I：

10.1214/lnms/1215090065

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：113 / 133

页数：21

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