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Cai, T. Tony; Low, Mark G.

Adaptive confidence balls. (English) Zbl 1091.62037

Ann. Stat. 34, No. 1, 202-228 (2006).
Summary: 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 \(\mathbb R^N\) and expected squared radius adapting over a maximum range of Besov bodies.

Cited in 39 Documents

MSC:

62G15 Nonparametric tolerance and confidence regions
62H12 Estimation in multivariate analysis
62F35 Robustness and adaptive procedures (parametric inference)

Keywords:

adaptive confidence balls; Besov body; block thresholding; coverage probability; expected squared radius; loss estimation
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References:

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