Statistics Papers

Document Type

Journal Article

Date of this Version

2004

Publication Source

The Annals of Statistics

Volume

32

Issue

2

Start Page

552

Last Page

576

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.

Keywords

Constrained risk inequality, linear functionals, minimax estimation, modulus of continuity, nonparametric functional estimation, white noise model

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Date Posted: 27 November 2017

This document has been peer reviewed.