Adaptive confidence bands

被引：29

作者：

Genovese, Christopher ^{[1
]}

Wasserman, Larry ^{[1
]}

机构：

[1] Carnegie Mellon Univ, Dept Stat, Pittsburgh, PA 15213 USA

来源：

ANNALS OF STATISTICS | 2008年 / 36卷 / 02期

基金：

美国国家科学基金会;

关键词：

nonparametric confidence bands; nonparametric regression; adaptive confidence sets; lower bounds;

D O I：

10.1214/07-AOS500

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：

We show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions. We propose instead to construct adaptive bands that cover a surrogate function f* which is close to, but simpler than, f. The surrogate captures the significant features in f. We establish lower bounds on the width for any confidence band for f* and construct a procedure that comes within a small constant factor of attaining the lower bound for finite-samples.

引用

页码：875 / 905

页数：31

共 38 条

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ANDREWS DWK, 2007, 1606 YALE U COWL FDN

[2] Confidence balls in Gaussian regression [J].