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
Recommended Citation
Cai, T., & Low, M. G. (2005). Nonquadratic Estimators of a Quadratic Functional. The Annals of Statistics, 33 (6), 2930-2956. http://dx.doi.org/10.1214/009053605000000147
Date Posted: 27 November 2017
This document has been peer reviewed.