Statistics Papers
Document Type
Journal Article
Date of this Version
2006
Publication Source
The Annals of Statistics
Volume
34
Issue
1
Start Page
202
Last Page
228
DOI
10.1214/009053606000000146
Abstract
Adaptive confidence balls are constructed for individual resolution levels as well as the entire mean vector in a multiresolution framework. Finite sample lower bounds are given for the minimum expected squared radius for confidence balls with a prespecified confidence level. The confidence balls are centered on adaptive estimators based on special local block thresholding rules. The radius is derived from an analysis of the loss of this adaptive estimator. In addition adaptive honest confidence balls are constructed which have guaranteed coverage probability over all of ℝN and expected squared radius adapting over a maximum range of Besov bodies.
Keywords
adaptive confidence balls, Besov body, block thresholding, coverage probability, expected squared radius, loss estimation
Recommended Citation
Cai, T., & Low, M. G. (2006). Adaptive Confidence Balls. The Annals of Statistics, 34 (1), 202-228. http://dx.doi.org/10.1214/009053606000000146
Date Posted: 27 November 2017
This document has been peer reviewed.