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On the Estimation of the Size of a Finite and Closed Population
Author(s) -
Bolfarine Heleno,
Leite José G.,
Rodrigues Josemar
Publication year - 1992
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710340507
Subject(s) - likelihood function , mathematics , maximum likelihood , likelihood principle , statistics , estimator , infinity , bayes estimator , maximum likelihood sequence estimation , estimation theory , bayesian information criterion , restricted maximum likelihood , bayesian probability , population , quasi maximum likelihood , mathematical analysis , demography , sociology
In this paper, we consider the problem of estimating the size N of a finite and closed population, using data obtained from capture‐recapture experiments. By defining an appropriate model, we investigate the maximum of the likelihood, of the profile likelihood and of an orthogonal adjusted profile likelihood (COX and REID, 1987) function. We show that they all may present infinity as the maximum likelihood estimator of N. This seems to be a characteristic of the likelihood approach in this problem. Further, we present a Bayesian approach with minimum prior information as a way of countering this difficulty. Exact analytical expressions for the posterior modes are also obtained.