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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.
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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 

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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