Maximum likelihood abundance estimation from capture-recapture data when covariates are missing at random

TL;DR

This paper introduces a maximum empirical likelihood method for estimating animal abundance in capture-recapture studies with missing covariate data, improving accuracy and confidence interval coverage over existing methods.

Contribution

It develops a novel maximum empirical likelihood estimator for abundance with missing covariates, demonstrating its asymptotic properties and superior performance in simulations.

Findings

Estimator has smaller mean square error than existing methods.

Empirical likelihood ratio confidence intervals have more accurate coverage.

Method successfully applied to bird species data.

Abstract

In capture-recapture experiments, individual covariates may be subject to missing, especially when the number of times of being captured is small. When the covariate information is missing at random, the inverse probability weighting method and multiple imputation method are widely used to obtain the point estimators of the abundance. These point estimators are then used to construct the Wald-type confidence intervals for the abundance. However, such intervals may have severely inaccurate coverage probabilities and their lower limits can be even less than the number of individuals ever captured. In this paper, we proposed a maximum empirical likelihood estimation approach for the abundance in presence of missing covariates. We show that the maximum empirical likelihood estimator is asymptotically normal, and that the empirical likelihood ratio statistic for abundance has a chisquare limiting distribution with one degree of freedom. Simulations indicate that the proposed estimator has smaller mean square error than the existing estimators, and the proposed empirical likelihood ratio confidence interval usually has more accurate coverage probabilities than the existing Wald-type confidence intervals. We illustrate the proposed method by analyzing the bird species yellow-bellied prinia collected in Hong Kong.