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Biometrika 1976 63(3):531-536; doi:10.1093/biomet/63.3.531
© 1976 by Biometrika Trust
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Efficient tests for branching processes

I. V. BASAWA and D. J. SCOTT

Department of Mathematics, La Trobe University Melbourne

This paper is concerned with efficiency in testing for the mean of the offspring distribution of a supercritical Galton-Watson process. It is suggested that the maximum likelihood estimator is generally inefficient for this problem in the sense that asymptotically it is not an optimum discriminator between alternative values of the parameter. Three competing tests are discussed and their efficiency compared via an example.

Key Words: Asymptotic efficiency • Inference for branching process • Maximum likelihood estimation • Power series distribution


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