Statistics Papers

Document Type

Journal Article

Date of this Version

2004

Publication Source

The Annals of Statistics

Volume

32

Issue

5

Start Page

1805

Last Page

1840

DOI

10.1214/009053604000000049

Abstract

A nonparametric adaptation theory is developed for the construction of confidence intervals for linear functionals. A between class modulus of continuity captures the expected length of adaptive confidence intervals. Sharp lower bounds are given for the expected length and an ordered modulus of continuity is used to construct adaptive confidence procedures which are within a constant factor of the lower bounds. In addition, minimax theory over nonconvex parameter spaces is developed.

Keywords

adaptation, between class modulus, confidence intervals, coverage, expected length, linear functionals, minimax estimation, modulus of continuity, white noise model

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Date Posted: 27 November 2017

This document has been peer reviewed.