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Biometrika 1971 58(3):499-508; doi:10.1093/biomet/58.3.499
© 1971 by Biometrika Trust
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The estimation of the probability of extinction and other parameters associated with branching processes

STEPHEN M. STIGLER

University of Wisconsin

Maximum likelihood estimates of the probability of the eventual extinction of a possibly age-dependent branching process are given for both the parametric and nonparametric cases, and their asymptotic properties derived. It is found that the nonparametric estimate performs very well relative to the parametric estimate in a large variety of situations, and therefore would often be preferable to the parametric estimate in view of the latter's lack of robustness.

Key Words: Galton-Watson process • Branching processes • Extinction probability • Multinomial distribution • Robust inference • Inference about branching processes


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