Statistics Papers

Document Type

Journal Article

Date of this Version

2006

Publication Source

The Annals of Statistics

Volume

34

Issue

5

Start Page

2298

Last Page

2325

DOI

10.1214/009053606000000849

Abstract

Adaptive estimation of a quadratic functional over both Besov and Lp balls is considered. A collection of nonquadratic estimators are developed which have useful bias and variance properties over individual Besov and Lp balls. An adaptive procedure is then constructed based on penalized maximization over this collection of nonquadratic estimators. This procedure is shown to be optimally rate adaptive over the entire range of Besov and Lp balls in the sense that it attains certain constrained risk bounds.

Keywords

adaptation, block thresholding, quadratic functionals, wavelets, white noise model

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Date Posted: 27 November 2017

This document has been peer reviewed.