The Annals of Statistics

Adaptive confidence balls

T. Tony Cai and Mark G. Low

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 34, Number 1 (2006), 202-228.

Dates
First available in Project Euclid: 2 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1146576261

Digital Object Identifier
doi:10.1214/009053606000000146

Mathematical Reviews number (MathSciNet)
MR2275240

Zentralblatt MATH identifier
1091.62037

Subjects
Primary: 62G99: None of the above, but in this section
Secondary: 62F12: Asymptotic properties of estimators 62F35: Robustness and adaptive procedures 62M99: None of the above, but in this section

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

Citation

Cai, T. Tony; Low, Mark G. Adaptive confidence balls. Ann. Statist. 34 (2006), no. 1, 202--228. doi:10.1214/009053606000000146. https://projecteuclid.org/euclid.aos/1146576261


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