Consider a supercritical Galton-Watson process $(Z_n)$ with offspring distribution a member of the power series family, and having unknown mean $\theta$. The conditional asymptotic normality of the suitably normalized maximum likelihood estimator of $\theta$ given the conditional information is established. The conditional information here is proportional to the total number of ancestors $V_n$, and it is also seen that this statistic is asymptotically ancillary for $\theta$ in a local sense. The proofs are via a detailed analysis of the joint characteristic function of $(Z_n, V_n)$, and the derivation serves to highlight the difficulties involved in establishing such conditional results generally.
Publié le : 1986-09-14
Classification:
Asymptotic conditional inference,
nonergodic models,
supercritical branching process,
maximum likelihood estimator,
asymptotic ancillarity,
60J80,
62F12
@article{1176350042,
author = {Sweeting, T. J.},
title = {Asymptotic Conditional Inference for the Offspring Mean of a Supercritical Galton-Watson Process},
journal = {Ann. Statist.},
volume = {14},
number = {2},
year = {1986},
pages = { 925-933},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350042}
}
Sweeting, T. J. Asymptotic Conditional Inference for the Offspring Mean of a Supercritical Galton-Watson Process. Ann. Statist., Tome 14 (1986) no. 2, pp. 925-933. http://gdmltest.u-ga.fr/item/1176350042/