On the estimation of population size under dependent dual-record system: an adjusted profile-likelihood approach

Abstract

Motivated by various applications in epidemiology, population studies, criminology, etc., the problem of estimating size of a homogeneous human population based on two-sample capture–recapture experiment is considered in this article. The Lincoln–Petersen estimate, assuming independence between the samples, is widely used though often its relevance is unanimously criticized. Time and behavioural response variation model (denoted by $M_{\mathrm{tb}}$) is the most suitable here. Effect of model mis-specification on the Lincoln–Petersen estimate is studied in terms of efficiency and robustness. We study the accuracy and efficiency of this estimator under existence of dependence between the samples. This article shows that profile-likelihood and its existing modifications fail to make inference from the model $M_{\mathrm{tb}}$. Therefore, an adjustment over profile likelihood is newly proposed and evaluated through an extensive simulation study. Finally, two real data sets with different characteristics are analyzed as practical illustrations of the proposed method.

Keywords:

• Adjusted profile likelihood
• human population
• incomplete data
• modified profile likelihood
• robustness
• behavioural response

2010 Mathematics Subject Classifications:

• 62F10
• 62H99
• 62P25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Integrated likelihood is another pseudo-likelihood method but we do not focus on it in the present article.

Additional information

Funding

10.13039/501100013357This study was supported by Indian Statistical Institute DS/JSTK-CC-0020F.