Geodesic
On the statistics of branching processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 3, pp. 623-633

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Let $\mu_t(n)$, $t=0,1,2,\dots,$ be a Galton–Watson process, starting from $n$ particles. We show that when $n,t\to\infty$ the estimator $$ \widehat A_t(n)=\frac{\sum_{k=1}^t\mu_k(n)}{\sum_{k=0}^{t-1}\mu_k(n)} $$ for the expectation $A=\mathbf E\mu_1(1)$ is consistent and asymptoticaly unbiased. We obtain limit distributions for $\widehat A_t(n)$ in the subcritical, critical and supercritical cases. 
@article{TVP_1975_20_3_a11,
     author = {N. M. Yanev},
     title = {On the statistics of branching processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {623--633},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_3_a11/}
}
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N. M. Yanev. On the statistics of branching processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 3, pp. 623-633. http://geodesic.mathdoc.fr/item/TVP_1975_20_3_a11/