Confidence balls in Gaussian regression

被引：32
|
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
收藏
页码：528 / 551
页数：24
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