%0 Electronic Article %A Zhang, Cun-Hui %I Institute of Mathematical Statistics %D 2005 %D 2005 %G English %@ 0090-5364 %~ Katalog UB TU-Chemnitz %T Estimation of Sums of Random Variables: Examples and Information Bounds %V 33 %J The Annals of Statistics %V 33 %N 5 %P 2022-2041 %U https://www.jstor.org/stable/3448633 %X

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.

%Z https://katalog.bibliothek.tu-chemnitz.de/Record/ai-55-aHR0cHM6Ly93d3cuanN0b3Iub3JnL3N0YWJsZS8zNDQ4NjMz %U https://katalog.bibliothek.tu-chemnitz.de/Record/ai-55-aHR0cHM6Ly93d3cuanN0b3Iub3JnL3N0YWJsZS8zNDQ4NjMz