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

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Date Posted: 27 November 2017

This document has been peer reviewed.