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May, 1979 Estimation Problems in Branching Processes with Random Environments
J. P. Dion, W. W. Esty
Ann. Statist. 7(3): 680-685 (May, 1979). DOI: 10.1214/aos/1176344688


Estimators are given for the two main parameters of the branching process with random environments, namely, the mean of the environmental mean (the average number of offspring per individual) and the mean of the logarithm of the environmental mean. The latter parameter indicates the certain extinction or possible explosion of the process. The consistency and asymptotic normality of the estimators are shown in the context of Smith and Wilkinson. Consistent estimators are also given for the corresponding variances and thus confidence intervals are obtained for the two main parameters of the system.


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J. P. Dion. W. W. Esty. "Estimation Problems in Branching Processes with Random Environments." Ann. Statist. 7 (3) 680 - 685, May, 1979.


Published: May, 1979
First available in Project Euclid: 12 April 2007

zbMATH: 0418.62069
MathSciNet: MR527502
Digital Object Identifier: 10.1214/aos/1176344688

Primary: 62M05
Secondary: 60J80

Keywords: branching process , consistency and asymptotic normality , estimation , random environment

Rights: Copyright © 1979 Institute of Mathematical Statistics

Vol.7 • No. 3 • May, 1979
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