非参数的高维两总体的同质性检验  

A Nonparametric Two-Sample Test for Homogeneity of Distributions in High Dimension

作　　者：李旭[1] 张宝学 LI Xu;ZHANG Baoxue(School of Mathematicsand Computer Science,Shanxi Normal University,Taiyuan 030031;Schoolof Statistics,Capital University of Economicsand Business,Beijing 100070)

机构地区：[1]山西师范大学数学与计算机科学学院,太原030031 [2]首都经济贸易大学统计学院,北京100070

出　　处：《系统科学与数学》2024年第8期2458-2475,共18页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(12271370,12071267);山西省自然科学基金(202203021222223,20210302124262,202103021245312)资助课题。

摘　　要：技术的进步使人们能够收集到大量的复杂数据对象,这些对象之间的同质性结构在统计学中有广泛的应用.然而,现有的一些同质性检验往往受到矩假设或调节参数的影响.为了克服这一限制,文章提出了一种新的高维两总体的同质性检验.基于重期望公式和特征函数的性质,论文构造了新的基于高维特征的同质性度量及其相应的检验统计量.进一步地,在一定的正则条件下,文章还建立了所提检验的大样本性质.如所提方法在原假设成立时是渐近卡方的,在备择假设下是渐近正态的.同时,蒙特卡罗模拟结果显示,对于高维数据,新检验比现有的几种方法具有更好的表现.Technological advances have enabled us to collect a lot of complex data objects,where homogeneity structure among these objects is widely used in Statistics.However,the existing metrics of homogeneity are subject to some qualifications,such as assumptions about the moment and parameters.To overcome the limitation,this paper proposes a new homogeneity test for high-dimensional two populations.Based on the double expectation formula and the properties of characteristic functions,a new measure and its empirical version are constructed in high-dimensional cases.Furthermore,under suitable regular conditions,the large sample nature of the proposed test is established too,such as the tests proposed in this paper converge to a mixture ofχ^(2) distributions under the null hypothesis and a normal distribution under the alternative hypothesis.Meanwhile,Monte Carlo simulation results show that the new methods perform better than several existing test procedures for high-dimensional data.

关 键 词：同质性检验 两样本问题 V统计量 置换检验 高维 

分 类 号：O212.1[理学—概率论与数理统计]