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April 2004 Minimax estimation of linear functionals over nonconvex parameter spaces
T. Tony Cai, Mark G. Low
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Ann. Statist. 32(2): 552-576 (April 2004). DOI: 10.1214/009053604000000094


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.


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T. Tony Cai. Mark G. Low. "Minimax estimation of linear functionals over nonconvex parameter spaces." Ann. Statist. 32 (2) 552 - 576, April 2004.


Published: April 2004
First available in Project Euclid: 28 April 2004

zbMATH: 1048.62054
MathSciNet: MR2060169
Digital Object Identifier: 10.1214/009053604000000094

Primary: 62G99
Secondary: 62C20 , 62F12 , 62M99

Keywords: Constrained risk inequality , linear functionals , minimax estimation , modulus of continuity , Nonparametric functional estimation , White noise model

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 2 • April 2004
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