A sharp adaptive confidence ball for self-similar functions

被引：16

作者：

Nickl, Richard ^{[1
]}

Szabo, Botond ^{[2
,3
]}

机构：

[1] Univ Cambridge, Cambridge CB2 1TN, England

[2] Univ Amsterdam, NL-1012 WX Amsterdam, Netherlands

[3] Budapest Univ Technol & Econ, Budapest, Hungary

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2016年 / 126卷 / 12期

关键词：

Adaptation; Confidence sets; BANDS; SETS; HONEST; REGRESSION; INTERVALS;

D O I：

10.1016/j.spa.2016.04.017

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：

In the nonparametric Gaussian sequence space model an l(2)-confidence ball C-n is constructed that adapts to unknown smoothness and Sobolev-norm of the infinite-dimensional parameter to be estimated. The confidence ball has exact and honest asymptotic coverage over appropriately defined 'self-similar' parameter spaces. It is shown by information-theoretic methods that this 'self-similarity' condition is weakest possible. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：3913 / 3934

页数：22

共 20 条

[1]

Bull AD, 2013, PROBAB THEORY REL, V156, P889, DOI 10.1007/s00440-012-0446-z

[2] Honest adaptive confidence bands and self-similar functions [J].