Accurate pivotals from recapture experiments with time variation

Abstract

Testing and confidence interval construction for a parameter are achieved by constructing a pivotal. In this paper we study construction of approximate pivotals from recapture models where capture probabilities possibly vary from occasion to occasion. We compare the asymptotic standard normality of various pivotals including analogues of the classical maximum likelihood/Wald, score and likelihood ratio statistics. Some bias adjustments are developed and indicate that the score pivotal has smaller bias than the pivotal of Chao (1989). The score and likelihood ratio pivotals both provide intervals with accurate two-sided coverage, but one-sided coverage accuracy varies. Chao's pivotal appears to be slightly conservative but is the simplest to compute. Classical pivotals based directly on the estimator are inadequate.