Estimation of sums of random variables: Examples and information bounds
| dc.creator | Zhang, Cun-Hui | |
| dc.date | 2006-02-10 | |
| dc.date.accessioned | 2026-07-07T08:07:31Z | |
| dc.date.available | 2026-07-07T08:07:31Z | |
| dc.description | This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models. An explicit relationship is established between efficient influence functions for the estimation of sums of variables and the estimation of their means. Certain ``plug-in'' estimators are proved to be asymptotically efficient in finite-dimensional models, while ``$u,v$'' estimators of Robbins are proved to be efficient in infinite-dimensional mixture models. Examples include certain species, network and data confidentiality problems. | |
| dc.description | Published at http://dx.doi.org/10.1214/009053605000000390 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/0602214 | |
| dc.identifier | http://arxiv.org/abs/math/0602214 | |
| dc.identifier | Annals of Statistics 2005, Vol. 33, No. 5, 2022-2041 | |
| dc.identifier | doi:10.1214/009053605000000390 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130960 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62F10, 62F12, 62G05, 62G20 (Primary) 62F15 (Secondary) | |
| dc.title | Estimation of sums of random variables: Examples and information bounds | |
| dc.type | text |