Estimating Population Size in a Continuous-time Removal Experiment with a Known Sub-population Size Ratio |
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Authors: | Liqun Xi Paul S F Yip Ray Watson |
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Institution: | (1) Department of Statistics and Actuarial Science, Hong Kong Faculty of Science, University of Hong Kong, Zhejiang University of Science, P. R. China;(2) Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong;(3) Department of Mathematics and Statistics, University of Melbourne, Australia |
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Abstract: | We study a continuous-time removal model for estimating the population size for a population in which a sub-population size
ratio is known. The maximum likelihood estimate and the optimal martingale estimate of the population size are obtained; these
are shown to be equivalent. A comparison between the proposed estimator and the maximum likelihood estimate which ignores
the information on the known size ratio is made, using a simulation study. The asymptotic variances of these two estimators
are also obtained, and a comparison between them is made. The sensitivity of mis-specification of the known size ratio is
examined. We also apply the corresponding discrete-time model to the proposed continuous-time setting, and study the efficiency
of the corresponding discrete-time type estimator relative to the proposed estimator. |
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Keywords: | Asymptotic variance Continuous-time Discrete-time Estimation efficiency Martingale MLE Population size estimation Removal experiment |
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