2005/12/01 by T. Tony Cai, Tommaso Cai, Mark G. Low · 1 citation
Engineering · Mathematics · #Advanced Control Systems Optimization #Control Systems and Identification #Statistical Methods and Inference #math.ST #msc:62F12 #msc:62F35 #msc:62G99 #msc:62M99 #stat.TH
paper · pdf · doi:10.1214/009053605000000147
published as Annals of Statistics 2005, Vol. 33, No. 6, 2930-2956 · Published at http://dx.doi.org/10.1214/009053605000000147 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2005/12/01 · arxiv created 2006/03/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.