  Sufficient statistics are derived for the population size and parameters of
commonly used closed population mark-recapture models. Rao-Blackwellization
details for improving estimators that are not functions of the statistics are
presented. As Rao-Blackwellization entails enumerating all sample reorderings
consistent with the sufficient statistic, Markov chain Monte Carlo resampling
procedures are provided to approximate the computationally intensive
estimators. Simulation studies demonstrate that significant improvements can be
made with the strategy. Supplementary materials for this article are available
online.
