Minimax Estimation Of Linear Functionals Over Nonconvex Parameter Spaces
The Annals of Statistics 32, 552 - 576, (2004).
Minimax Estimation Of Linear Functionals Over Nonconvex Parameter Spaces
The Annals of Statistics 32, 552 - 576, (2004).
- 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.
- Paper: pdf file.
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