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Partition structures and sufficient statistics

Part of: Limit theorems Stochastic processes Parametric inference

Published online by Cambridge University Press:  14 July 2016

Paul Joyce
Paul Joyce*
Affiliation:
University of Idaho
*
∗Postal address: Department of Mathematics and Statistics, University of Idaho, Moscow, ID 83843, USA. Email address: joyce@uidaho.edu.
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Abstract

Is the Ewens distribution the only one-parameter family of partition structures where the total number of types sampled is a sufficient statistic? In general, the answer is no. It is shown that all counterexamples can be generated via an urn scheme. The urn scheme need only satisfy two general conditions. In fact, the conditions are both necessary and sufficient. However, in particular, for a large class of partition structures that naturally arise in the infinite alleles theory of population genetics, the Ewens distribution is the only one in this class where the total number of types is sufficient for estimating the mutation rate. Finally, asymptotic sufficiency for parametric families of partition structures is discussed.

Keywords

Infinite alleles modelexchangeable equivalence relationssufficient statisticspartition structures

MSC classification

Primary: 62F05: Asymptotic properties of tests
Secondary: 60G42: Martingales with discrete parameter 60F15: Strong theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 3 , September 1998 , pp. 622 - 632
Copyright
Copyright © Applied Probability Trust 1998 

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Footnotes

This research is supported by National Science Foundation grant DMS 96–26764.

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