SEQUENTIAL ESTIMATION FOR BRANCHING-PROCESSES WITH IMMIGRATION
成果类型：
Article
署名作者：
SRIRAM, TN; BASAWA, IV; HUGGINS, RM
署名单位：
La Trobe University
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176348395
发表日期：
1991
页码：
2232-2243
关键词：
摘要：
For the critical and subcritical Galton-Watson processes with immigration, it is shown that if the data were collected according to an appropriate stopping rule, the natural sequential estimator of the offspring mean m is asymptotically normally distributed for each fixed m is-an-element-of (0, 1]. Furthermore, the sequential estimator is shown to be asymptotically normally distributed uniformly over a class of offspring distributions with m is-an=element-of (0, 1] bounded variance and satisfying a mild condition. These results are to be contrasted with the nonsequential approach where drastically different limit distributions are obtained for the two cases: (a) m < 1 (normal) and (b) m = 1 (nonnormal), thus leading to a singularity problem at m = 1. The sequential approach proposed here avoids this singularity and unifies the two cases. The proof of the uniformity result is based on a uniform version of the well-known Anscombe's theorem.