Limit laws of estimators for critical multi-type Galton-Watson processes

• 成果类型: Article
• 署名作者: Chi, ZY
• 署名单位: University of Chicago
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000521
• 发表日期: 2004
• 页码: 1992-2015
• 关键词: increasing random number; branching-processes; immigration; ancestors; THEOREMS

摘要

We consider the asymptotics of various estimators based on a large sample of branching trees from a critical multi-type Galton-Watson process, as the sample size increases to infinity. The asymptotics of additive functions of trees, such as sizes of trees and frequencies of types within trees, a higher-order asymptotic of the relative frequency estimator of the left eigenvector of the mean matrix, a higher-order joint asymptotic of the maximum likelihood estimators of the offspring probabilities and the consistency of an estimator of the right eigenvector of the mean matrix, are established.