Inference on population size in binomial detectability models

• 成果类型: Article
• 署名作者: Fewster, R. M.; Jupp, P. E.
• 署名单位: University of Auckland; University of St Andrews
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asp051
• 发表日期: 2009
• 页码: 805820
• 关键词: capture-recapture; behavioral-response

摘要

Many models for biological populations, including simple mark-recapture models and distance sampling models, involve a binomially distributed number, n, of observations x(1), ..., x(n) on members of a population of size N. Two popular estimators of (N, theta), where theta is a vector parameter, are the maximum likelihood estimator ((N) over cap, (theta) over cap) and the conditional maximum likelihood estimator ((N) over cap (c) (theta) over cap (c)) based on the conditional distribution of x(1), ..., x(n) given n. We derive the large-N asymptotic distributions of (((N) over cap, (theta) over cap) and ((N) over cap (c) (theta) over cap (c)), and give formulae for the biases of log (N) over cap and log (N) over cap (c). We show that the difference (N) over capc -(N) over cap is, remarkably, of order 1 and we give a simple formula for the leading part of this difference. Simulations indicate that in many cases this formula is very accurate and that confidence intervals based on the asymptotic distribution have excellent coverage. An extension to product-binomial models is given.