Maximum‐likelihood estimation for the removal method

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.