title: On population size estimators in the Poisson mixture model.
abstract: Estimating population sizes via capture-recapture experiments has enormous applications. The Poisson mixture model can be adopted for those applications with a single list in which individuals appear one or more times. We compare several nonparametric estimators, including the Chao estimator, the Zelterman estimator, two jackknife estimators and the bootstrap estimator. The target parameter of the Chao estimator is a lower bound of the population size. Those of the other four estimators are not lower bounds, and they may produce lower confidence limits for the population size with poor coverage probabilities. A simulation study is reported and two examples are investigated.
authors.affiliation: School of Statistics and Management, and Center for Social Security Studies, Shanghai University of Finance and Economics, Shanghai, 200433, China.
authors.forename: Chang Xuan
authors.initials: CX
authors.lastname: Mao
authors.forename: Nan
authors.initials: N
authors.lastname: Yang
authors.forename: Jinhua
authors.initials: J
authors.lastname: Zhong
mesh_terms: D015982:Bias; D001699:Biometry / Q000379:methods; D003198:Computer Simulation; D016001:Confidence Intervals; D006556:Heroin Dependence / Q000453:epidemiology; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D016012:Poisson Distribution; D011156:Population Density; D018709:Statistics, Nonparametric; D013785:Thailand / Q000453:epidemiology; D014904:Western Australia / Q000453:epidemiology
keywords: Capture-recapture; Lower bounds; Lower confidence limits