Semiparametric empirical likelihood inference for abundance from one-inflated capture-recapture data

Area of Science:

• Ecology
• Biostatistics
• Statistical Modeling

Background:

• Abundance estimation using capture-recapture data is crucial across disciplines.
• Existing methods struggle with one-inflation and heterogeneity, leading to unstable estimators and poor confidence interval coverage.
• One-inflated zero-truncated count models are often used but have limitations.

Purpose of the Study:

• To propose a novel semiparametric empirical likelihood (EL) approach for abundance estimation.
• To address challenges of one-inflation and heterogeneity in capture-recapture data analysis.
• To develop a more powerful score test for detecting one-inflation.

Main Methods:

• Developed a semiparametric empirical likelihood (EL) method for one-inflated binomial and Poisson regression models.
• Implemented an expectation-maximization algorithm to facilitate EL computation.
• Proposed and proved the asymptotic normality of a new score test for one-inflation.

Main Results:

• The proposed score test demonstrates greater power compared to existing methods.
• The maximum empirical likelihood (EL) estimator exhibits a smaller mean square error.
• Simulation studies confirm the superior performance of the proposed methods.

Conclusions:

• The novel empirical likelihood (EL) approach provides a more stable and accurate method for abundance estimation.
• The developed score test effectively identifies one-inflation in ecological and epidemiological data.
• The methods are validated through real-world data analyses, showing practical utility.