期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2016
卷号：78
期号：2
页码：248-268
DOI：10.1007/s13171-016-0082-2
语种：English
出版社：Indian Statistical Institute
摘要：The paper discusses the joint estimation of two important parameters of the offspring distribution namely mean and variance of a controlled branching process or ϕ branching process. The estimation of these parameters was separately carried out by Gonzalez et al. ( Test , 13 (2), 465–479, ( 2004 ), Test , 14 (1), 199–213, ( 2005 )). The present article is an attempt to show that, the estimators proposed by these authors are also optimal in the sense of estimating functions ( O F optimality). The joint O A optimality, that is; joint asymptotic properties of these estimators are also established using martingale limit theory. The joint O A optimality in special case, a model proposed by Dion and Essebbar ( 1995 ) for controlled branching process is also discussed.
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