The simplicial depth, like other relevant multivariate statistical data depth functions, vanishes right outside the convex hull of the support of the distribution with respect to which the depth is computed. This is problematic when it is required to differentiate among points outside the convex hull of the distribution support, with respect to which the depth is computed, based on their depth values. We provide the first proposal for simplicial depth which do not vanish right outside the convex hull of the distribution. The properties of the proposal and of the corresponding estimator are studied theoretically and by means of Monte Carlo simulations and analysis of datasets.

翻译：单纯形深度，如同其他相关的多元统计数据深度函数一样，在用于计算深度的分布支撑的凸包之外会立即消失。当需要根据深度值区分位于该凸包之外的点时，这一特性便产生了问题。我们首次提出了一种单纯形深度的新方案，该方案在分布支撑凸包之外不会立即消失。我们通过理论分析、蒙特卡洛模拟以及数据集分析，对所提方案及其对应估计量的性质进行了研究。