Estimating the prediction function and the number of unseen species in sampling with replacement

• 成果类型: Article
• 署名作者: Boneh, S; Boneh, A; Caron, RJ
• 署名单位: Technion Israel Institute of Technology; University of Windsor
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2669633
• 发表日期: 1998
• 页码: 372-379
• 关键词: shakespeare

摘要

A sample of N units is taken from a population consisting of an unknown number of species. We are interested in estimating the number of species and the prediction function for future sampling. The prediction function is defined as the expected number of new species that will be found if an additional sample of size tN is taken for any positive real number t. In this paper we point out that an estimator suggested by Efron and Thisted lacks some essential properties of the true prediction function, for example, the property of alternating copositivity. As a result it cannot be used for large values of t. We propose an alternative estimator that possesses the essential properties and is easily obtained. We illustrate our estimator with two numerical examples and a simulation study.