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September, 1986 Asymptotic Conditional Inference for the Offspring Mean of a Supercritical Galton-Watson Process
T. J. Sweeting
Ann. Statist. 14(3): 925-933 (September, 1986). DOI: 10.1214/aos/1176350042

Abstract

Consider a supercritical Galton-Watson process $(Z_n)$ with offspring distribution a member of the power series family, and having unknown mean $\theta$. The conditional asymptotic normality of the suitably normalized maximum likelihood estimator of $\theta$ given the conditional information is established. The conditional information here is proportional to the total number of ancestors $V_n$, and it is also seen that this statistic is asymptotically ancillary for $\theta$ in a local sense. The proofs are via a detailed analysis of the joint characteristic function of $(Z_n, V_n)$, and the derivation serves to highlight the difficulties involved in establishing such conditional results generally.

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T. J. Sweeting. "Asymptotic Conditional Inference for the Offspring Mean of a Supercritical Galton-Watson Process." Ann. Statist. 14 (3) 925 - 933, September, 1986. https://doi.org/10.1214/aos/1176350042

Information

Published: September, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0633.62084
MathSciNet: MR856798
Digital Object Identifier: 10.1214/aos/1176350042

Subjects:
Primary: 60J80
Secondary: 62F12

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 3 • September, 1986
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