A Parametric Bootstrap for the Mean Measure of Divergence

TL;DR

This paper introduces a parametric bootstrap method for the Mean Measure of Divergence, leveraging the Anscombe transformation to improve analysis of small or incomplete anthropological samples.

Contribution

It develops a new parametric bootstrap technique based on the normal approximation of transformed divergence measures, enhancing analysis with limited data.

Findings

The method performs well with artificial data.

It is effective on real anthropological datasets.

Provides more powerful results than non-parametric approaches.

Abstract

For more than $50$ years the {\it 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 $ \theta $, obtained from the Anscombe transformation to stabilize the variance, nearly follows a normal distribution with zero mean and variance $ \sigma^2 = 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 $ \theta $ 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.