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October 2006 Optimal adaptive estimation of a quadratic functional
T. Tony Cai, Mark G. Low
Ann. Statist. 34(5): 2298-2325 (October 2006). 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.

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T. Tony Cai. Mark G. Low. "Optimal adaptive estimation of a quadratic functional." Ann. Statist. 34 (5) 2298 - 2325, October 2006. https://doi.org/10.1214/009053606000000849

Information

Published: October 2006
First available in Project Euclid: 23 January 2007

zbMATH: 1110.62048
MathSciNet: MR2291501
Digital Object Identifier: 10.1214/009053606000000849

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

Keywords: Adaptation , block thresholding , quadratic functionals , Wavelets , White noise model

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 5 • October 2006
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