Nonparametric Density Estimation for Capture-Recapture

Capture-recapture (CRC) is a way to estimate the size of a population by combining multiple incomplete lists of population units. Accurate estimators must model dependence between lists. One kind of dependence is unit-level list dependence, in which previous capture directly reduces the probability of subsequent capture. Another kind of dependence arises indirectly from the heterogeneity in capture probabilities across units. Existing nonparametric CRC methods do not allow both kinds of dependence to depend on covariates. We fill this gap with a new two-stage approach. In the first stage, we estimate the conditional densities of the capture pattern as a function of the covariates. In the second stage, we impute the conditional density of the unobserved capture pattern (no captures) by applying a log-linear models locally. A Horvitz-Thompson style population estimator follows.