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Licensed Unlicensed Requires Authentication Published by De Gruyter March 18, 2020

A Parametric Bootstrap for the Mean Measure of Divergence

  • F. Zertuche ORCID logo EMAIL logo and A. Meza-Peñaloza

Abstract

For more than 50 years the Mean Measure of Divergence (MMD) has been one of the most prominent tools used in anthropology for the study of non-metric traits. However, one of the problems, in anthropology including palaeoanthropology (more often there), is the lack of big enough samples or the existence of samples without sufficiently measured traits. Since 1969, with the advent of bootstrapping techniques, this issue has been tackled successfully in many different ways. Here, we present a parametric bootstrap technique based on the fact that the transformed θ, obtained from the Anscombe transformation to stabilize the variance, nearly follows a normal distribution with standard deviation σ = 1 / N + 1 / 2 , where N is the size of the measured trait. When the probabilistic distribution is known, parametric procedures offer more powerful results than non-parametric ones. We profit from knowing the probabilistic distribution of θ to develop a parametric bootstrapping method. We explain it carefully with mathematical support. We give examples, both with artificial data and with real ones. Our results show that this parametric bootstrap procedure is a powerful tool to study samples with scarcity of data.

Acknowledgements

This work is supported in part by PAPIIT project No. IN402720. The authors thank Pilar López Rico for her informatics services; Fernando González Hernández, Rubén González Zainez, and Patricia Peláez Flores for their computer advise.

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Supplementary Material

The online version of this article offers supplementary material (DOI:https://doi.org/10.1515/ijb-2019-0117).


Received: 2019-10-09
Revised: 2020-01-03
Accepted: 2020-02-28
Published Online: 2020-03-18

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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