基于符号秩的高维均值检验  

Signed-rank-based test for high dimensional mean vector

作　　者：刘琰 李仕明[3] 张三国[1,2] LIU Yan;LI Shiming;ZHANG Sanguo(School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China;Key Laboratory of Big Data Mining and Knowledge Management,Chinese Academy of Sciences,Beijing 100049,China;Beijing Tongren Eye Center,Beijing Tongren Hospital,Capital Medical University,Beijing 100730,China)

机构地区：[1]中国科学院大学数学科学学院,北京100049 [2]中国科学院大数据挖掘与知识管理重点实验室,北京100049 [3]首都医科大学附属北京同仁医院眼科中心,北京100730

出　　处：《中国科学院大学学报（中英文）》2022年第5期586-592,共7页Journal of University of Chinese Academy of Sciences

基　　金：Supported by Beijing Natural Science Foundation(Z190004,JQ20029);Key Program of Joint Funds of the National Natural Science Foundation of China(U19B2040);Capital Health Research and Development of Special(2020-2-1081)。

摘　　要：研究高维情形下一样本均值检验的问题。已有的一些高维均值检验方法假设样本具有椭球等高分布。为应用到更多的分布,提出基于符号秩的均值检验统计量。所提方法是稳健的且具有刻度变换不变性。建立了所提出检验统计量的渐近性质,数值模拟表明该方法可以很好地控制第一类错误,且功效更高。还将该方法应用到眼科数据中。This work is concerned with tests for one-sample mean vectors under high dimensional cases.Existing high dimensional tests for mean vectors base on the assumption of elliptical distribution have been proposed recently.To extend to more distributions,we propose a signed-rankbased test.The proposed test statistic is robust and scalar-invariant.Asymptotic properties of the test statistic are established.Numerical studies show that the proposed test has a good control of the type-I error and is more efficiency.We also employ the proposed method to analyze an ophthalmic data.

关 键 词：高维数据分析 符号秩 一样本检验 标度不变性 

分 类 号：O212.1[理学—概率论与数理统计]