Optimal adaptive estimation of a quadratic functional

The Annals of Statistics · 2006 · Volume 34 · Issue 5

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.

Keywords

62F12, 62F35, 62G99, 62M99, Adaptation, block thresholding, quadratic functionals, Wavelets, White noise model

Enable JavaScript for citation tools and additional paper interactions.