Estimation of sums of random variables: Examples and information bounds

Details Estimation of sums of random variables: Examples and information bounds Estimation of sums of random variables: Examples and information bounds

2006-02-10

arxiv.org/abs/math/0602214v1

Annals of Statistics 2005, Vol. 33, No. 5, 2022-2041

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000390 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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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