The Annals of Statistics
- Ann. Statist.
- Volume 34, Number 5 (2006), 2298-2325.
Optimal adaptive estimation of a quadratic functional
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.
Ann. Statist., Volume 34, Number 5 (2006), 2298-2325.
First available in Project Euclid: 23 January 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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