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.
Publié le : 1975-09-14
Classification:
62.15,
62.70,
60.67,
Branching process,
estimation of variance,
estimation of mean,
asymptotic normality,
maximum likelihood estimation
@article{1176343250,
author = {Dion, Jean-Pierre},
title = {Estimation of the Variance of a Branching Process},
journal = {Ann. Statist.},
volume = {3},
number = {1},
year = {1975},
pages = { 1183-1187},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343250}
}
Dion, Jean-Pierre. Estimation of the Variance of a Branching Process. Ann. Statist., Tome 3 (1975) no. 1, pp. 1183-1187. http://gdmltest.u-ga.fr/item/1176343250/