An Application of Profile-Likelihood Based Confidence Interval to Capture-Recapture Estimators

In recent years, more robust methods 'of estimating the size of a closed population (N) from capture-recapturedata have been developed. However, interval estimation for N has seen few practical developments. The usual approach for constructing a confidence interval, known as a Wahl confidence interval, is based on the assumption of asymptotic normality. It is well bown that the small sample distribution of capture-recaptu es­ timators are strongly asymmetric and thus deviate from normality. As a resuI~ Wald confidence intervals are frequently unreasonable; having lower limits that extend below the number of animals known to exis~ or even being negative. Two other approaches to the construction of confidence intervals, the profi1e..Jikelihood based method and the bootstrapped method, show much promise. The computational burden of the profile­ likelihood confidence interval is much less than the bootstrapped confidence interval and appears to be an excellent alternative to the Wald confidence interval.