Estimation of sums of random variables: Examples and information bounds

• 成果类型: Article
• 署名作者: Zhang, CH
• 署名单位: Rutgers University System; Rutgers University New Brunswick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000390
• 发表日期: 2005
• 页码: 2022-2041
• 关键词: NUMBER

摘要

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.