Adaptive confidence balls

The Annals of Statistics · 2006 · Volume 34 · Issue 1

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

62F12, 62F35, 62G99, 62M99, Adaptive confidence balls, Besov body, block thresholding, coverage probability, expected squared radius, loss estimation

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