Confidence balls in Gaussian regression

被引：33

作者：

Baraud, Y ^{[1
]}

机构：

[1] Ecole Normale Super, Dept Math & Applicat, CNRS, UMR 8553, F-75230 Paris 05, France

来源：

ANNALS OF STATISTICS | 2004年 / 32卷 / 02期

关键词：

confidence ball; nonparametric regression; hypothesis testing; estimation;

D O I：

10.1214/009053604000000085

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：

Starting from the observation of an R(n)-Gaussian vector of mean f and covariance matrix sigma(2)I(n) (I(n) is the identity matrix), we propose a method for building a Euclidean confidence ball around f, with prescribed probability of coverage. For each n, we describe its nonasymptotic property and show its optimality with respect to some criteria.

引用

页码：528 / 551

页数：24

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