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