期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2012
卷号：74
期号：1
页码：80-100
DOI：10.1007/s13171-012-0012-x
语种：English
出版社：Indian Statistical Institute
摘要：We consider the classic problem of estimating T , the total number of species in a population, from repeated counts in a simple random sample. We first show that the frequently used Chao-Lee estimator can in fact be obtained by Bayesian methods with a Dirichlet prior, and then use such clarification to develop a new estimator; numerical tests and some real experiments show that the new estimator is more flexible than existing ones, in the sense that it adapts to changes in the normalized interspecies variance γ 2. Our method involves simultaneous estimation of T , γ 2, and of the parameter λ in the Dirichlet prior, and the only limitation seems to come from the required convergence of the prior which imposes the restriction γ 2 ≤ 1. We also obtain confidence intervals for T and an estimation of the species’ distribution. Some numerical examples are given, together with applications to sampling from a Census database closely following Benford’s law, showing good performances of the new estimator, even beyond γ 2 = 1. Tests on confidence intervals show that the coverage frequency appears to be in good agreement with the desired confidence level.
关键词：Bayesian posterior ; confidence interval ; Dirichlet prior ; point estimator ; simple random sample ; unobserved species ; unobserved probability
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