Nonparametric Estimation of the Probability of Discovering a New Species

摘要

A random sample is taken from a population consisting of an unknown number of distinct species. A quantity of interest is the probability of discovering a new species when an additional draw from the population is made. An estimator of this quantity was introduced by Starr (1979). This document proves a conjecture of Starr's that the estimator is uniformly minimum variance unbiased and give various asymptotic properties of the estimator. A nonparametric maximum likelihood estimator is introduced which has similar asymptotic properties. A Monte-Carlo study is given which suggests guidelines for choosing an estimator under various circumstances. Keywords: U statistics.