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December 2005 Nonquadratic estimators of a quadratic functional
T. Tony Cai, Mark G. Low
Ann. Statist. 33(6): 2930-2956 (December 2005). 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.

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T. Tony Cai. Mark G. Low. "Nonquadratic estimators of a quadratic functional." Ann. Statist. 33 (6) 2930 - 2956, December 2005. https://doi.org/10.1214/009053605000000147

Information

Published: December 2005
First available in Project Euclid: 17 February 2006

zbMATH: 1085.62055
MathSciNet: MR2253108
Digital Object Identifier: 10.1214/009053605000000147

Subjects:
Primary: 62G99
Secondary: 62F12 , 62F35 , 62M99

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

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 6 • December 2005
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