2006/02/01 by T. Tony Cai, Mark G. Low · 2 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Distributed Sensor Networks and Detection Algorithms #Financial Risk and Volatility Modeling #Statistical Methods and Inference #math.ST #msc:62F12 #msc:62F35 #msc:62G99 #msc:62M99 #stat.TH
paper · pdf · doi:10.1214/009053606000000146
published as Annals of Statistics 2006, Vol. 34, No. 1, 202-228 · Published at http://dx.doi.org/10.1214/009053606000000146 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2006/02/01 · arxiv created 2006/05/17 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.