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 $\sigma = 1 / \sqrt{N + 1/2}$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.

中文翻译：

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平均散度度量的参数自举法


50 多年来，平均差异度量 (MMD) 一直是人类学中用于研究非度量特征的最重要的工具之一。然而，人类学，包括古人类学（更常见）的问题之一是缺乏足够大的样本或存在没有充分测量特征的样本。自 1969 年以来，随着引导技术的出现，这个问题已经通过多种不同的方式成功解决。在这里，我们提出了一种参数引导技术，基于以下事实：从 Anscombe 变换获得的用于稳定方差的变换 θ 几乎遵循标准差 $\sigma = 1 / \sqrt{N + 1/2} 的正态分布$σ=1/N+1/2，其中N是测量特征的大小。当概率分布已知时，参数过程比非参数过程提供更强大的结果。我们通过了解 θ 的概率分布来开发参数引导方法。我们在数学支持下仔细解释它。我们给出了一些例子，包括人工数据和真实数据。我们的结果表明，这种参数引导程序是研究数据稀缺样本的强大工具。