基于能量距离法的多维分类变量的分布差异检验  

Testing the distributional difference of two multi-dimensional categorical variables based on the energy distance

作　　者：彭东海[1] 张留伟[2] PENG Dong-hai;ZHANG Liu-wei(College of Mathematics,Zhongshan Polytechnic,Zhongshan 528404,China;College of Geospatial Engineering and Science,Sun Yat-sen University,Zhuhai 519082,China)

机构地区：[1]中山职业技术学院数学教研室,广东中山528404 [2]中山大学测绘学院,广东珠海519082

出　　处：《湖北师范大学学报（自然科学版）》2022年第3期10-17,共8页Journal of Hubei Normal University：Natural Science

基　　金：中山职业技术学院科研项目(2019KQ17)。

摘　　要：通过引入虚拟向量,将两个分类变量的分布差异检验问题等价地转换成两个虚拟向量的分布差异检验。基于这两个虚拟向量的能量距离,给出了一种新的简便的检验方法,采用置换样本的程序计算检验法的p值。数值模拟显示,相比传统的卡方检验法,新的检验方法不受样本频数列联表中各单元格的频数的影响,因而大部分时候具有更高的功效。最后,给出该方法在两个多维分类向量的分布差异检验中的应用。By introducing two dummy vectors,the problem of testing the distributional difference of two categorical variables can be transformed equivalently into the test of distributional difference of two dummy vectors.Based on the energy distance of the two dummy vectors,a new and simple test is proposed,and the p value of the test is calculated by using the permutation procedure.Numerical simulation shows that,compared with the traditional Chi-square test,the new test is not affected by the frequency of each cell in the sample frequency contingency table,so it often has higher power in most cases.Finally,the test can be applied to a real data to test the distributional difference of two multidimensional categorical vectors.

关 键 词：分类变量 分布差异 能量距离 卡方检验 置换程序 

分 类 号：O212.4[理学—概率论与数理统计]