Statistics Papers

Document Type

Journal Article

Date of this Version

2005

Publication Source

The Annals of Statistics

Volume

33

Issue

5

Start Page

2311

Last Page

2343

DOI

10.1214/009053605000000633

Abstract

Adaptive estimation of linear functionals over a collection of parameter spaces is considered. A between-class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability over two parameter spaces in the same way that the usual modulus of continuity captures the minimax difficulty of estimation over a single parameter space. A general construction of optimally adaptive estimators based on an ordered modulus of continuity is given. The results are complemented by several illustrative examples.

Keywords

adaptive estimation, between-class modulus of continuity, cost of adaptation, linear functional, ordered modulus of continuity, white noise model

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Date Posted: 27 November 2017

This document has been peer reviewed.