An adaptation theory for nonparametric confidence intervals

被引：56

作者：

Cai, TT ^{[1
]}

Low, MG ^{[1
]}

机构：

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

来源：

ANNALS OF STATISTICS | 2004年 / 32卷 / 05期

关键词：

adaptation; between class modulus; confidence intervals; coverage; expected length; linear functionals; minimax estimation; modulus of continuity; white noise model;

D O I：

10.1214/00905360400000049

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：

A nonparametric adaptation theory is developed for the construction of confidence intervals for linear functionals. A between class modulus of continuity captures the expected length of adaptive confidence intervals. Sharp lower bounds are given for the expected length and an ordered modulus of continuity is used to construct adaptive confidence procedures which are within a constant factor of the lower bounds. In addition, minimax theory over nonconvex parameter spaces is developed.

引用

页码：1805 / 1840

页数：36

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