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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

Abstract

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. https://doi.org/10.1214/009053604000000094

Information

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

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

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

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 2 • April 2004
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