Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-14T04:25:46.117Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimating the large mutation parameter of the Ewens sampling formula

Part of:Limit theoremsParametric 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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 1 , March 2017, pp. 42 - 54
Copyright
Copyright © Applied Probability Trust 2017 

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