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October 2005 Estimation of sums of random variables: Examples and information bounds
Cun-Hui Zhang
Ann. Statist. 33(5): 2022-2041 (October 2005). DOI: 10.1214/009053605000000390


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.


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Cun-Hui Zhang. "Estimation of sums of random variables: Examples and information bounds." Ann. Statist. 33 (5) 2022 - 2041, October 2005.


Published: October 2005
First available in Project Euclid: 25 November 2005

zbMATH: 1086.62035
MathSciNet: MR2211078
Digital Object Identifier: 10.1214/009053605000000390

Primary: 62F10 , 62F12 , 62G05 , 62G20
Secondary: 62F15

Keywords: data confidentiality , Disclosure risk , efficient estimation , Empirical Bayes , influence function , information bound , networks , node degree , species problem , sum of variables , Utility

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 5 • October 2005
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