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

TL;DR

This paper advances the theoretical understanding of the M0 capture-recapture model by proposing a Rao-Blackwellized estimator based on sufficient statistics, with minimal practical impact but significant theoretical contribution.

Contribution

It introduces a Rao-Blackwellized estimator for the M0 model using sufficient statistics, enhancing theoretical insights into capture-recapture estimation.

Findings

The improved estimator is theoretically justified.

Practical improvements on estimates are likely negligible.

Provides simulation code for further research.

Abstract

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.