Estimation of sums of random variables: Examples and information bounds

By Cun-Hui Zhang. 2005

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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.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/82d6dedaedef42b6c345ca423271822ac113e6df