A Contribution to the Theory Behind the Capture-Recapture M0 Model: An Improved Estimator

We explore the use of a sufficient statistic based on the data of samples that are selected under the M_0 capture-recapture closed population model (Schwarz and Seber, 1999). A Rao-Blackwellized version of the estimator based on a sufficient statistic is then presented. Though the improvements made on the preliminary capture-recapture estimates are likely to be negligible, this body of work is primarily intended to contribute to the theory around the capture-recapture models. The code for a simulation is provided in the appendix.