The Annals of Statistics

Estimation of the Variance of a Branching Process

Jean-Pierre Dion

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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.

Article information

Source
Ann. Statist., Volume 3, Number 5 (1975), 1183-1187.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343250

Digital Object Identifier
doi:10.1214/aos/1176343250

Mathematical Reviews number (MathSciNet)
MR378308

Zentralblatt MATH identifier
0359.62067

JSTOR
links.jstor.org

Keywords
62.15 62.70 60.67 Branching process estimation of variance estimation of mean asymptotic normality maximum likelihood estimation

Citation

Dion, Jean-Pierre. Estimation of the Variance of a Branching Process. Ann. Statist. 3 (1975), no. 5, 1183--1187. doi:10.1214/aos/1176343250. https://projecteuclid.org/euclid.aos/1176343250


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