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Robustness of the Ewens sampling formula. (English) Zbl 0836.62022

Summary: Under the assumptions of the neutral infinite alleles model, \(K\) (the total number of alleles present in a sample) is sufficient for estimating \(\theta\) (the mutation rate). This is a direct result of the Ewens sampling formula, which gives a consistent, asymptotically normal estimator for \(\theta\) based on \(K\). It is shown that the same estimator used to estimate \(\theta\) under neutrality is consistent and asymptotically normal, even when the assumption of selective neutrality is violated.

MSC:

62F12 Asymptotic properties of parametric estimators
60G42 Martingales with discrete parameter
60F15 Strong limit theorems
62P10 Applications of statistics to biology and medical sciences; meta analysis
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