Bias correction in multiple-systems estimation

TL;DR

This paper introduces a new bias correction estimator for multiple-systems estimation with three or more sources, improving accuracy in small samples and impacting population size estimates.

Contribution

It extends Chapman's bias correction estimator to multiple sources beyond two, demonstrating superior performance through simulations and real data application.

Findings

The new estimator reduces bias significantly in small samples.

Simulation results show improved accuracy over existing estimators.

Application to homelessness data demonstrates practical impact.

Abstract

If part of a population is hidden but two or more sources are available that each cover parts of this population, dual- or multiple-system(s) estimation can be applied to estimate this population. For this it is common to use the log-linear model, estimated with maximum likelihood. These maximum likelihood estimates are based on a non-linear model and therefore suffer from finite-sample bias, which can be substantial in case of small samples or a small population size. This problem was recognised by Chapman, who derived an estimator with good small sample properties in case of two available sources. However, he did not derive an estimator for more than two sources. We propose an estimator that is an extension of Chapman's estimator to three or more sources and compare this estimator with other bias-reduced estimators in a simulation study. The proposed estimator performs well, and much better than the other estimators. A real data example on homelessness in the Netherlands shows that our proposed model can make a substantial difference.