Identification of multitype branching processes

• 成果类型: Article
• 署名作者: Maaouia, F; Touati, A
• 署名单位: Universite de Tunis-El-Manar; Faculte des Sciences de Tunis (FST)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000561
• 发表日期: 2005
• 页码: 2655-2694
• 关键词: galton-watson processes; central-limit-theorem; martingales; CONVERGENCE; estimator; variance

摘要

We solve the problem of constructing an asymptotic global confidence region for the means and the covariance matrices of the reproduction distributions involved in a supercritical multitype branching process. Our approach is based on a central limit theorem associated with a quadratic law of large numbers performed by the maximum likelihood or the multidimensional Lotka-Nagaev estimator of the reproduction law means. The extension of this approach to the least squares estimator of the mean matrix is also briefly discussed.