Minimax estimation of linear functionals over nonconvex parameter spaces

Details Minimax estimation of linear functionals over nonconvex parameter spaces Minimax estimation of linear functionals over nonconvex parameter spaces

2004-06-22

arxiv.org/abs/math/0406427v1

Annals of Statistics 2004, Vol. 32, No. 2, 552-576

Mathematics

Statistics Theory

Scientific paper

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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