Estimating population size from capture-recapture studies via sample coverage and estimating functions

This paper presents a method of inference for the population size in a capture-recapture experiment in continuous time. A class of estimators for the population size is generated by a martingale estimating function with the notion of sample coverage. It includes the existing estimators suggested by Yip and Becker and Heyde for model Mt which allows the capture intensities to vary with time. Also, it gives a new estimator for model Mth which allows heterogeneous capture intensities varying with time as well. Optimal estimators of population size for each model are discussed. A simulation study is used to assess the performance of the proposed procedure.