Analysis of a capture-recapture estimator for the size of populations with heterogenous catchability, and its evaluation on RDS data from rural Uganda

In this paper, we consider capture-recapture experiments with heterogenous catchability. In the setting we consider, the widespread Huggins-Alho estimator is not very suitable and we introduce and study a new generalized Horvitz-Thompson estimator. Our motivation is Respondent Driven Sampling (RDS), a prime example for such a setting where the capture probability is dependent on both the unknown population size as well as on an observable covariate, the network degree of an individual, due to peer recruitment. After discussing the theoretical properties of the new estimator, with full details given in the appendix, we evaluate it on various empirical and simulated data-sets, focusing on an RDS survey in a population in rural Uganda in which the population size is known a priori. The results thus obtained demonstrate that the adjusted estimator is less biased than the naive Lincoln-Petersen estimator.