On adaptive estimation of linear functionals

被引：24

作者：

Cai, TT ^{[1
]}

Low, MG ^{[1
]}

机构：

[1] Univ Penn, Wharton Sch, Dept Stat, Philadelphia, PA 19104 USA

来源：

ANNALS OF STATISTICS | 2005年 / 33卷 / 05期

关键词：

adaptive estimation; between-class modulus of continuity; cost of adaptation; linear functional; ordered modulus of continuity; white noise model;

D O I：

10.1214/009053605000000633

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：

Adaptive estimation of linear functionals over a collection of parameter spaces is considered. A between-class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability over two parameter spaces in the same way that the usual modulus Of Continuity captures the minimax difficulty of estimation over a single parameter space. A general construction of optimally adaptive estimators based on an ordered modulus of continuity is given. The results are complemented by several illustrative examples.

引用

页码：2311 / 2343

页数：33

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