瓦瑟斯坦度量空间统计学前奏曲

Chon Van Le, U. Pham
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引用次数: 0

摘要

目的 本文的主要目的是向应用统计学家和计量经济学家介绍当前使用非欧几里得数据集的研究方法。具体来说,它提供了在瓦瑟斯坦空间中进行统计的基础和原理,其中概率度量的度量是最优传输理论中产生的瓦瑟斯坦度量。作者阐述了在(随机)概率度量的数据空间中使用瓦瑟斯坦度量的基础和原理。研究结果在阐述对非欧几里得数据集的新统计分析时,论文说明了按照弗雷谢特方案对统计推断的传统方面进行的概括。原创性/价值除了阐述新数据分析的研究方法外,论文还讨论了瓦瑟斯坦度量在金融风险度量稳健性方面的应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A prelude to statistics in Wasserstein metric spaces
PurposeThis paper aims mainly at introducing applied statisticians and econometricians to the current research methodology with non-Euclidean data sets. Specifically, it provides the basis and rationale for statistics in Wasserstein space, where the metric on probability measures is taken as a Wasserstein metric arising from optimal transport theory.Design/methodology/approachThe authors spell out the basis and rationale for using Wasserstein metrics on the data space of (random) probability measures.FindingsIn elaborating the new statistical analysis of non-Euclidean data sets, the paper illustrates the generalization of traditional aspects of statistical inference following Frechet's program.Originality/valueBesides the elaboration of research methodology for a new data analysis, the paper discusses the applications of Wasserstein metrics to the robustness of financial risk measures.
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