Estimating the Prediction Function and the Number of Unseen Species in Sampling with Replacement
针对有放回抽样中未知物种数问题，指出Efron和Thisted估计量缺乏交替共正性等关键性质，提出一种更优的替代估计量，并通过数值例子和模拟验证。
Abstract 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. Key Words: Alternating copositivityCoverageDetectionEstimating population size