## The Annals of Statistics

#### 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

https://projecteuclid.org/euclid.aos/1169571798

Digital Object Identifier
doi:10.1214/009053606000000849

Mathematical Reviews number (MathSciNet)
MR2291501

Zentralblatt MATH identifier
1110.62048

#### 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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