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Estimating the large mutation parameter of the Ewens sampling formula

Part of: Limit theorems Parametric inference

Published online by Cambridge University Press:  04 April 2017

Koji Tsukuda
Koji Tsukuda*
Affiliation:
Kurume University
*
* Current address: Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, Japan. Email address: k.tsukuda@gmail.com
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Abstract

We derive some limit theorems associated with the Ewens sampling formula when its parameter is increasing together with a sample size. Moreover, the limit results are applied in order to investigate asymptotic properties of the maximum likelihood estimator.

Keywords

Asymptotic properties of estimatorsmaximum likelihood estimationEwens sampling formula

MSC classification

Primary: 62F12: Asymptotic properties of estimators
Secondary: 60F05: Central limit and other weak theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 1 , March 2017 , pp. 42 - 54
Copyright
Copyright © Applied Probability Trust 2017 

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References

[1] Ewens, W. J. (1972).The sampling theory of selectively neutral alleles.Theoret. Pop. Biol. 3,87–112.Google Scholar
[2] Feng, S. (2007).Large deviations associated with Poisson–Dirichlet distribution and Ewens sampling formula.Ann. Appl. Prob. 17,1570–1595.CrossRefGoogle Scholar
[3] Griffiths, R. C. (1979).On the distribution of allele frequencies in a diffusion model.Theoret. Pop. Biol. 15,140–158.Google Scholar
[4] Hoppe, F. M. (1984).Pólya-like urns and the Ewens’ sampling formula.J. Math. Biol. 20,91–94.Google Scholar
[5] Joyce, P., Krone, S. M. and Kurtz, T. G. (2002).Gaussian limits associated with the Poisson–Dirichlet distribution and the Ewens sampling formula.Ann. Appl. Prob. 12,101–124.CrossRefGoogle Scholar
[6] Van der Vaart, A. W. (1998).Asymptotic Statistics.Cambridge University Press.Google Scholar
[7] Watterson, G. A. (1974).The sampling theory of selectively neutral alleles.Adv. Appl. Prob. 6,463–488.Google Scholar
[8] Yamato, H. (2013).Edgeworth expansions for the number of distinct components associated with the Ewens sampling formula.J. Japan Statist. Soc. 43,17–28.CrossRefGoogle Scholar