Petersen estimator, Chapman adjustment, list effects, and heterogeneity

We use a nonparametric mixture model for the purpose of estimating the size of a population from multiple lists in which both the individual effects and list effects are allowed to vary. We propose a lower bound of the population size that admits an analytic expression. The lower bound can be estimated without the necessity of model-fitting. The asymptotical normality of the estimator is established. Both the estimator itself and that for the estimable bound of its variance are adjusted. These adjusted versions are shown to be unbiased in the limit. Simulation experiments are performed to assess the proposed approach and real applications are studied.