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February 2006 Adaptive confidence balls
T. Tony Cai, Mark G. Low
Ann. Statist. 34(1): 202-228 (February 2006). 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.

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T. Tony Cai. Mark G. Low. "Adaptive confidence balls." Ann. Statist. 34 (1) 202 - 228, February 2006. https://doi.org/10.1214/009053606000000146

Information

Published: February 2006
First available in Project Euclid: 2 May 2006

zbMATH: 1091.62037
MathSciNet: MR2275240
Digital Object Identifier: 10.1214/009053606000000146

Subjects:
Primary: 62G99
Secondary: 62F12 , 62F35 , 62M99

Keywords: Adaptive confidence balls , Besov body , block thresholding , coverage probability , expected squared radius , loss estimation

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 1 • February 2006
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