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Estimation for Continuous Branching Processes
Author(s) -
Overbeck Ludger
Publication year - 1998
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00092
Subject(s) - mathematics , branching process , estimator , asymptotic distribution , exponential family , branching (polymer chemistry) , inference , consistency (knowledge bases) , strong consistency , statistical inference , maximum likelihood , population , exponential function , econometrics , statistics , mathematical analysis , discrete mathematics , materials science , demography , epistemology , sociology , composite material , philosophy
The maximum‐likelihood estimator for the curved exponential family given by continuous branching processes with immigration is investigated. These processes originated from population biology but also model the dynamics of interest rates and development of the state of technology in economics. It is proved that in contrast to branching processes with discrete space and/or time the MLE gives a unified approach to the inference. In order to include singular subdomains of the parameter space we modify the MLE slightly. Consistency and asymptotic normality for the MLE are considered. Concerning the asymptotic theory of the experiments, all three properties LAQ, LAN, and LAMN occur for different submodels