## The Annals of Statistics

### Estimation of the Variance of a Branching Process

Jean-Pierre Dion

#### 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

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