Population Size Estimation Using Zero-Truncated Poisson Regression with Measurement Error

Wen-Han Hwang, Jakub Stoklosa and Ching-Yun Wang ()
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Wen-Han Hwang: National Chung Hsing University
Jakub Stoklosa: The University of New South Wales
Ching-Yun Wang: Fred Hutchinson Cancer Research Center

Journal of Agricultural, Biological and Environmental Statistics, 2022, vol. 27, issue 2, No 6, 303-320

Abstract: Abstract Population size estimation is an important research field in biological sciences. In practice, covariates are often measured upon capture on individuals sampled from the population. However, some biological measurements, such as body weight, may vary over time within a subject’s capture history. This can be treated as a population size estimation problem in the presence of covariate measurement error. We show that if the unobserved true covariate and measurement error are both normally distributed, then a naïve estimator without taking into account measurement error will under-estimate the population size. We then develop new methods to correct for the effect of measurement errors. In particular, we present a conditional score and a nonparametric corrected score approach that are both consistent for population size estimation. Importantly, the proposed approaches do not require the distribution assumption on the true covariates; furthermore, the latter does not require normality assumptions on the measurement errors. This is highly relevant in biological applications, as the distribution of covariates is often non-normal or unknown. We investigate finite sample performance of the new estimators via extensive simulated studies. The methods are applied to real data from a capture–recapture study. Supplementary materials accompanying this paper appear on-line.

Keywords: Capture–recapture data; Corrected score; Errors-in-variables; Weighted partial likelihood (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13253-021-00481-z

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