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Optimal estimation of the criticality parameter of a supercritical branching process having random environments

Published online by Cambridge University Press:  14 July 2016

Anthony G. Pakes  and
C. C. Heyde
Anthony G. Pakes*
Affiliation:
University of Western Australia
C. C. Heyde*
Affiliation:
CSIRO Division of Mathematics and Statistics
*
∗ Postal address: Department of Mathematics, University of Western Australia, Nedlands, WA 6009, Australia.
∗∗ Postal address: CSIRO Division of Mathematics and Statistics, P.O. Box 1965, Canberra City, ACT 2601, Australia.
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Abstract

Let {Zn} be a Galton-Watson process with i.i.d. random environments. This paper is concerned with estimation of π= E log Mn, where Mn is the. conditional expected number of offspring per nth generation individual, given the environments, when this quantity is positive. We show that, given non-extinction, {n-1 log Zn} is asymptotically the most efficient estimator of πamongst a broad class of those that are linear combinations of {log Zi: 1 ≦ j ≦ n}·

Keywords

BRANCHING PROCESSRANDOM ENVIRONMENTSESTIMATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 2 , June 1982 , pp. 415 - 420
Copyright
Copyright © Applied Probability Trust 1982 

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References

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