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.
Publié le : 2005-10-14
Classification:
Empirical Bayes,
sum of variables,
utility,
efficient estimation,
information bound,
influence function,
species problem,
networks,
node degree,
data confidentiality,
disclosure risk,
62F10,
62F12,
62G05,
62G20,
62F15
@article{1132936555,
author = {Zhang, Cun-Hui},
title = {Estimation of sums of random variables: Examples and information bounds},
journal = {Ann. Statist.},
volume = {33},
number = {1},
year = {2005},
pages = { 2022-2041},
language = {en},
url = {http://dml.mathdoc.fr/item/1132936555}
}
Zhang, Cun-Hui. Estimation of sums of random variables: Examples and information bounds. Ann. Statist., Tome 33 (2005) no. 1, pp. 2022-2041. http://gdmltest.u-ga.fr/item/1132936555/