Asymptotic conditional inference for the offspring mean of a supercritical Galton-Watson process
The supercritical Galton-Watson process with unknown mean is one of the well known examples of a nonergodic statistical model, i.e. the maximum likelihood estimator is asymptotically mixed normal under classical nonrandom norming. In the paper conditional asymptotic normality of the ML estimator given the conditional information is established. The approach is not the same as that considered by \textit{I. V. Basawa} and \textit{P. J. Brockwell}, Ann. Stat. 12, 161-171 (1984; Zbl 0546.62059), who conditioned on the (unobservable) normed limit information.
scientific article; zbMATH DE number 4030767