2004/04/01 by T. Tony Cai, Mark G. Low · 3 citations
Engineering · Mathematics · #Advanced Control Systems Optimization #Control Systems and Identification #Stability and Control of Uncertain Systems #math.ST #msc:62C20 #msc:62F12 #msc:62G99 #msc:62M99. #stat.TH
paper · pdf · doi:10.1214/009053604000000094
published as Annals of Statistics 2004, Vol. 32, No. 2, 552-576
openalex publication_date 2004/04/01 · arxiv created 2004/06/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The minimax theory for estimating linear functionals is extended to the case of a finite union of convex parameter spaces. Upper and lower bounds for the minimax risk can still be described in terms of a modulus of continuity. However in contrast to the theory for convex parameter spaces rate optimal procedures are often required to be nonlinear. A construction of such nonlinear procedures is given. The results developed in this paper have important applications to the theory of adaptation.