Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-06-25T05:58:59.685Z Has data issue: false hasContentIssue false
  • English
  • Français

On the non-existence of consistent estimates in Galton-Watson processes

Published online by Cambridge University Press:  14 July 2016

Richard Lockhart
Richard Lockhart*
Affiliation:
Simon Fraser University
*
∗ Postal address: Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada.
Get access Rights & Permissions [Opens in a new window]

Abstract

Estimation of the offspring distribution from a single realization of a supercritical Galton-Watson process is studied. It is shown that, based on population totals, a parameter of the offspring distribution cannot be estimated unless it is determined by the mean, variance, lattice size and lattice offset of the offspring distribution.

Keywords

CONSISTENT ESTIMATIONSUPERCRITICAL GALTON-WATSON PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 4 , December 1982 , pp. 842 - 846
Copyright
Copyright © Applied Probability Trust 1982 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This research was supported, in part, by NSERC Grant No. A4023.

References

Heyde, C. C. (1974) On estimating the variance of the offspring distribution in a simple branching process. Adv. Appl. Prob. 6, 421–433.Google Scholar
Petrov, V. V. (1964) On local limit theorems for sums of independent random variables. Theory Prob. Appl. 9, 312–320.CrossRefGoogle Scholar