Date of this Version
The Annals of Statistics
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.
adaptation, block thresholding, quadratic functionals, wavelets, white noise model
Cai, T., & Low, M. G. (2006). Optimal Adaptive Estimation of a Quadratic Functional. The Annals of Statistics, 34 (5), 2298-2325. http://dx.doi.org/10.1214/009053606000000849
Date Posted: 27 November 2017
This document has been peer reviewed.