Nonquadratic estimators of a quadratic functional
| dc.creator | Cai, T. Tony | |
| dc.creator | Low, Mark G. | |
| dc.date | 2006-03-06 | |
| dc.date.accessioned | 2026-07-07T08:07:38Z | |
| dc.date.available | 2026-07-07T08:07:38Z | |
| dc.description | 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. | |
| dc.description | 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) | |
| dc.identifier | https://arxiv.org/abs/math/0603134 | |
| dc.identifier | http://arxiv.org/abs/math/0603134 | |
| dc.identifier | Annals of Statistics 2005, Vol. 33, No. 6, 2930-2956 | |
| dc.identifier | doi:10.1214/009053605000000147 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130999 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G99 (Primary) 62F12, 62F35, 62M99 (Secondary) | |
| dc.title | Nonquadratic estimators of a quadratic functional | |
| dc.type | text |