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Minimax estimation of linear functionals over nonconvex parameter spaces

T. Tony Cai·Mark G. Low
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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. 2004-06-22. Minimax estimation of linear functionals over nonconvex parameter spaces. https://doi.org/10.1214/009053604000000094

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