A semi-parametric maximum-likelihood analysis of measurement error in population size estimation

Abstract

This work addresses the challenge of measurement errors in capture–recapture (CR) studies with covariates. These errors can introduce bias and undermine inference quality. To address this issue, we introduce a nonparametric measurement error model tailored to the ‘repeated counts’ setting, employing EM-type algorithms for parameter estimation. We use the Horvitz–Thompson estimator for population size estimates. Rigorous simulations, covering varying degrees of measurement error reliability, confirm our approach’s effectiveness. Applied to benchmark datasets, it consistently provides more accurate point estimates and robust uncertainty quantification, enhancing the reliability of CR analyses.