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September, 1975 Estimation of the Variance of a Branching Process
Jean-Pierre Dion
Ann. Statist. 3(5): 1183-1187 (September, 1975). DOI: 10.1214/aos/1176343250

Abstract

Assume given the $(n + 1)$-first generation sizes of a supercritical branching process. An estimator is proposed for the variance $\sigma^2$ of this process when the mean is known. It is shown to be unbiased, consistent and asymptotically normal. From that one deduces a consistent and asymptotically normal estimator for $\sigma^2$ in the case of an unknown mean. Finally, the maximum likelihood estimator of $\sigma^2$, based on a richer sample, is found and asymptotic properties are studied.

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Jean-Pierre Dion. "Estimation of the Variance of a Branching Process." Ann. Statist. 3 (5) 1183 - 1187, September, 1975. https://doi.org/10.1214/aos/1176343250

Information

Published: September, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0359.62067
MathSciNet: MR378308
Digital Object Identifier: 10.1214/aos/1176343250

Keywords: 60.67 , 62.15 , 62.70 , asymptotic normality , branching process , estimation of mean , estimation of variance , maximum likelihood estimation

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 5 • September, 1975
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