Maximum likelihood estimation of the offspring variance
in a Bienaymé-Galton-Watson branching process
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Maximum likelihood estimation of the offspring variance
in a Bienaymé-Galton-Watson branching process
Peter Guttorp
Department of Statistics, GN-22
University of Washington
Seattle, WA 98195
USA
Richard A. Lockhart
Department of Mathematics and Statistics
Simon Fraser University
Burnaby, BC V5A 1S6
Canada
Abstract:
An algorithm for the computation of a maximum likelihood estimate
of the offspring distribution in a
Bienaymé-Galton-Watson branching process is presented. Although
the
offspring distribution in general is not consistently estimable
(even conditional upon non-extinction), the invariance of
maximum likelihood estimators allows for estimation of the
offspring
variance as the variance of the estimated offspring distribution. The
variance is (conditionally) consistently estimable assuming fairly
strong regularity conditions.
The proof uses a new local limit theorem for discrete random
variables, which is uniform over distributions
of different lattice size.
Richard Lockhart
Thu Oct 26 23:26:04 PDT 1995