摘要
对于一维数据,很容易对数据进行排序.在高维情况下,文章定义了"最小向量"并通过比较每个样本与"最小向量"之间的欧式距离对高维数据进行排序赋秩.对高维两样本位置参数是否相同的假设检验问题,根据所提出的数据排序方法将一维Wilcoxon-MannWhitney秩和检验推广到高维情形.与其他位置检验方法相比,方法具有不依赖于分布,平移,缩放不变的特性,同时能良好应用于高维小样本的位置检验问题.理论上,文章证明该检验统计量在原假设下的渐近分布是正态分布及在一些弱相依条件下证明了该检验具有良好的功效.数值分析结果表明,对于不同总体分布的位置参数是否相等的检验问题,所提出的检验具有更好的有效性.
It is simple to sort the sample for univariate data.In this paper,we define the"minimum vector"and rank the high-dimensional data by comparing the Euclidean distance between each sample and the"minimum vector".For checking the adequacy whether the two-sample location parameter with high dimension is equal,the one-dimensional Wilcoxon Mann Whitney rank sum test is extended to the highdimensional case according to the proposed data sorting method.Compared with other existing methods,the proposed test is distribution free and can be applied to high-dimension,low-sample-size situations.What’s more,the new approach has the property of translation and scale invariance.In theory,we prove that the proposed statistic is normal distribution asymptotically under null hypothesis.The behavior of the test under alternative hypothesis is also investigated under some weakly conditions.The numerical analysis show that the proposed test is superior to the compared statistics in almost all scenarios.
作者
邱涛
吴文琦
许王莉
QIU Tao;WU Wenqi;XU Wangli(School of Statistics,Renmin University of China,Beijing 100872;Center for Applied Statistics,Renmin University of China,Beijing 100872)
出处
《系统科学与数学》
CSCD
北大核心
2020年第12期2445-2458,共14页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金项目(11971478)
教育部人文社会科学重点研究基地重大项目(16JJD910002)
“中央高校建设世界一流大学(学科)和特色发展引导专项资金”(KYGJD2019003)
北京市自然科学基金(Z190002)
中国人民大学公共健康与疾病预防控制交叉学科重大创新平台建设成果资助课题。
