Date of this Version
The Annals of Statistics
Estimation of a quadratic functional over parameter spaces that are not quadratically convex is considered. It is shown, in contrast to the theory for quadratically convex parameter spaces, that optimal quadratic rules are often rate suboptimal. In such cases minimax rate optimal procedures are constructed based on local thresholding. These nonquadratic procedures are sometimes fully efficient even when optimal quadratic rules have slow rates of convergence. Moreover, it is shown that when estimating a quadratic functional nonquadratic procedures may exhibit different elbow phenomena than quadratic procedures.
Besov balls, Gaussian sequence model, information bound, minimax estimation, quadratic functional, quadratic estimators
Cai, T., & Low, M. G. (2005). Nonquadratic Estimators of a Quadratic Functional. The Annals of Statistics, 33 (6), 2930-2956. http://dx.doi.org/10.1214/009053605000000147
Date Posted: 27 November 2017
This document has been peer reviewed.