Asymptotic conditional inference for the offspring mean of a supercritical Galton-Watson process
type: Item
instance of: scholarly article
title: Asymptotic conditional inference for the offspring mean of a supercritical Galton-Watson process
zbMATH Open document ID: 0633.62084
published in: The Annals of Statistics
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62M05
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 4030767
zbMATH Keywords: asymptotic conditional inference
zbMATH Keywords: asymptotic ancillarity
zbMATH Keywords: supercritical Galton-Watson process
zbMATH Keywords: unknown mean
zbMATH Keywords: nonergodic statistical model
zbMATH Keywords: maximum likelihood estimator
zbMATH Keywords: conditional asymptotic normality
author: Trevor Sweeting
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350042
OpenAlex ID: W2037614175
DOI: 10.1214/AOS/1176350042
description: scientific article; zbMATH DE number 4030767