Statistics Papers

Document Type

Journal Article

Date of this Version

2005

Publication Source

The Annals of Statistics

Volume

33

Issue

6

Start Page

2930

Last Page

2956

DOI

10.1214/009053605000000147

Abstract

Estimation of a quadratic functional over parameter spaces that are not quadratically convex is considered. It is shown, in contrast to the theory for quadratically convex parameter spaces, that optimal quadratic rules are often rate suboptimal. In such cases minimax rate optimal procedures are constructed based on local thresholding. These nonquadratic procedures are sometimes fully efficient even when optimal quadratic rules have slow rates of convergence. Moreover, it is shown that when estimating a quadratic functional nonquadratic procedures may exhibit different elbow phenomena than quadratic procedures.

Keywords

Besov balls, Gaussian sequence model, information bound, minimax estimation, quadratic functional, quadratic estimators

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Date Posted: 27 November 2017

This document has been peer reviewed.