Semiparametric Estimation of Tag Loss and Reporting Rates for Tag-Recovery Experiments Using Exact Time-at-Liberty Data

We present a semiparametric likelihood approach to estimating reporting rates and tag-loss rates from the tags returned from capture-recapture studies. Such studies are commonly used to estimate critical population parameters. Tag loss rates are estimated using double-tagged animals, while reporting rates are estimated using information from high-reward tags. A likelihood function is constructed based on the conditional distribution of the type of tag returned (low or high reward, single or double tag), given that a tag has been returned. This involves many sparse 5 x 1 tag-return contingency tables, and choosing a good functional form for the tag loss rate is difficult with such data. We model tag-loss rates using monotone-smoothing splines, and use these nonparametric estimates to diagnose the parametric form of the tag-loss rate. The nonparametric methods can also be used directly to model tag-loss rates.