Minimax estimation of linear functionals over nonconvex parameter spaces
Statistics Theory
2007-06-13 v1 Statistics Theory
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.
Cite
@article{arxiv.math/0406427,
title = {Minimax estimation of linear functionals over nonconvex parameter spaces},
author = {T. Tony Cai and Mark G. Low},
journal= {arXiv preprint arXiv:math/0406427},
year = {2007}
}