Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T19:54:35.322Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

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.)

References

Athreya, K. B. and Ney, P. E. (1972) Branching Processes. Springer-Verlag, Berlin.Google Scholar
Becker, N. (1977) Estimation for discrete time branching processes with application to epidemics. Biometrics 33, 515–522.Google Scholar
Chow, Y. S. and Teicher, H. (1978) Probability Theory. Springer-Verlag, Berlin.Google Scholar
Dion, J. P. and Esty, W. (1979) Estimation problems in branching processes with random environments. Ann. Statist. 7, 680–685.CrossRefGoogle Scholar
Nanthi, K. (1979) Estimation of the criticality parameter of a supercritical branching process with random environments. J. Appl. Prob. 16, 890–896.CrossRefGoogle Scholar
Rao, C. R. (1965) Linear Statistical Inference and its Applications. Wiley, New York.Google Scholar