The Annals of Statistics

Optimal adaptive estimation of a quadratic functional

T. Tony Cai and Mark G. Low

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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.

Article information

Source
Ann. Statist., Volume 34, Number 5 (2006), 2298-2325.

Dates
First available in Project Euclid: 23 January 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1169571798

Digital Object Identifier
doi:10.1214/009053606000000849

Mathematical Reviews number (MathSciNet)
MR2291501

Zentralblatt MATH identifier
1110.62048

Subjects
Primary: 62G99: None of the above, but in this section
Secondary: 62F12: Asymptotic properties of estimators 62F35: Robustness and adaptive procedures 62M99: None of the above, but in this section

Keywords
Adaptation block thresholding quadratic functionals wavelets white noise model

Citation

Cai, T. Tony; Low, Mark G. Optimal adaptive estimation of a quadratic functional. Ann. Statist. 34 (2006), no. 5, 2298--2325. doi:10.1214/009053606000000849. https://projecteuclid.org/euclid.aos/1169571798


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