On Posterior Asymptotic Normality and Asymptotic Normality of Estimators for the Galton-Watson Process
David Scott · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1987
SUMMARY For a Galton-Watson process with offspring distribution pθ, where θ is an unknown parameter, asymptotic posterior normality is established for θ and for the mean of the offspring distribution. A form of asymptotic normality for the mean of the offspring distribution is also obtained, without restriction on whether the process is supercritical or not, provided that the total number of offspring increases to infinity. A non-Bayesian procedure is suggested for testing for supercriticality of the Galton-Watson process.