两独立样本的非参数检验的一些新进展及展望
Non-Parametric Two-Sample Tests: Recent Developments and Prospects
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摘要: 当今数据爆发式地增长, 不仅挑战着传统统计推断的理论和方法, 而且拓广了统计推断的研究范畴. 如何对各种类型的数据进行科学地差异性分析是统计推断研究的一个重要领域, 作为差异性分析的主要工具——两样本检验一直是研究的重点和热点. 但以往的大部分研究是围绕着欧氏数据展开的, 而对于非欧氏数据的研究则是刚刚起步. 本文尝试总结一些现有的非参数两样本检验的内在规律, 由此构造新的两样本的非参数检验, 可用于结构更为复杂的数据. 此外, 本文还讨论此研究方向所面临的挑战.Abstract: The advancement of cutting-edge technology produces huge data sets. The current data boom not only poses a challenge to the traditional theory of statistical inference but also expands its scope. An important area of statistical inference research is difference analysis using various data types. The two-sample test is the primary tool for difference analysis, which has always been the focus and hot spot in the statistical community. However, previous research on the two-sample test has been focused on Euclidean data, whereas related studies on non-Euclidean data are still in their infancy. This study reviews some common characteristics of existing nonparametric two-sample tests. Then, based on this information, we create new two-sample nonparametric tests for data with more complex structures. In addition, the problems facing this field of study are discussed.