Summary
This paper is concerned with efficiency in the estimation of the mean θ of the offspring distribution of a supercritical Galton–Watson branching process on the basis of a sample of n consecutive generation sizes. First, a direct comparison is made between the maximum likelihood estimator and the simple ratio of generation sizes estimator. Next, a new definition of asymptotic efficiency of an estimator is given, generalizing that of Rao (1973). It is shown that, for offspring distributions belonging to the class of power series distributions, the maximum likelihood estimator is efficient in this new sense. The paper concludes with some remarks on the implications of this theory in the estimation of the growth rate in a pure birth process.
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[Received February 1974. Revised October 1974]
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Heyde, C.C. (2010). Remarks on efficiency in estimation for branching processes. In: Maller, R., Basawa, I., Hall, P., Seneta, E. (eds) Selected Works of C.C. Heyde. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5823-5_38
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DOI: https://doi.org/10.1007/978-1-4419-5823-5_38
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