Adaptive Confidence Balls
Tony Cai and Mark Low
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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 $\RR^N$ and expected squared radius adapting over a maximum range of Besov bodies.
- Paper:
pdf file.
- Other related papers:
Cai, T. & Low, M. (2005).
Non-quadratic estimators of a quadratic functional.
The Annals of Statistics 33, 2930-2956. - Cai, T. & Low, M. (2006).
Optimal adaptive estimation of a quadratic functional.
The Annals of Statistics 34, 2298-2325.