2006/02/01 by James Robins, Aad van der Vaart · 1 citation
Mathematics · #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical Methods in Clinical Trials #math.ST #msc:62F25 #msc:62G15 #msc:62G20 #stat.TH
paper · pdf · doi:10.1214/009053605000000877
published as Annals of Statistics 2006, Vol. 34, No. 1, 229-253 · Published at http://dx.doi.org/10.1214/009053605000000877 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 2026/08/01
We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection of models. The latter adaptation is necessarily limited in scope. We review the notion of adaptive confidence regions, and relate the optimal rates of the diameter of adaptive confidence regions to the minimax rates for testing and estimation. Applications include the finite normal mean model, the white noise model, density estimation and regression with random design.