| Abstract: | We prove that the profile log-likelihood function for the removal method of estimating population size is unimodal. The result is obtained by a variation-diminishing property of the Laplace transform. An implication of this result is that the likelihood-ratio confidence region for the population size is always an interval. Necessary and sufficient conditions for the existence of a finite maximum-likelihood estimator are presented. We also present evidence that the likelihood-ratio confidence interval for the population size has acceptable small-sample coverage properties. |
