高维条件下两样本均值的Neyman截断检验

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
Ping Dong, Lu Lin
{"title":"高维条件下两样本均值的Neyman截断检验","authors":"Ping Dong, Lu Lin","doi":"10.1214/21-bjps519","DOIUrl":null,"url":null,"abstract":"Abstract. Multivariate two-sample testing problems often arise from the statistical analysis for scientific data, especially for bioinformatics data. To detect components with different values between two mean vectors, well-known procedures are to apply Sum-of-Squares type tests, such as Hotelling’s T 2-test. However, such a test is not suitable to high dimensional settings because of singular covariance matrix and accumulated errors. Nowadays, a lot of test methods for high dimensional data are developed, mainly including two types, Sum-of-Squares type and Max type. The Sum-of-Squares type test statistics have poor performance against sparse alternatives. And the Max type test statistic is not powerful enough to deal with non-sparse datasets. In this paper, we propose a Max-Partial-Sum type statistic named Neyman’s Truncation test, which is conducted by maximum partial sums of marginal test statistics. Besides non-sparse datasets, Neyman’s Truncation test also has great power against dense and sparse alternatives. The asymptotic distribution of the test statistic under null hypothesis is obtained and the power of the test is analyzed. To avoid the slow convergence rate of the asymptotic distribution, we realize our method by Bootstrap procedures. Simulation studies and the analysis of leukemia dataset are carried out to verify the numerical performance.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Neyman’s truncation test for two-sample means under high dimensional setting\",\"authors\":\"Ping Dong, Lu Lin\",\"doi\":\"10.1214/21-bjps519\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. Multivariate two-sample testing problems often arise from the statistical analysis for scientific data, especially for bioinformatics data. To detect components with different values between two mean vectors, well-known procedures are to apply Sum-of-Squares type tests, such as Hotelling’s T 2-test. However, such a test is not suitable to high dimensional settings because of singular covariance matrix and accumulated errors. Nowadays, a lot of test methods for high dimensional data are developed, mainly including two types, Sum-of-Squares type and Max type. The Sum-of-Squares type test statistics have poor performance against sparse alternatives. And the Max type test statistic is not powerful enough to deal with non-sparse datasets. In this paper, we propose a Max-Partial-Sum type statistic named Neyman’s Truncation test, which is conducted by maximum partial sums of marginal test statistics. Besides non-sparse datasets, Neyman’s Truncation test also has great power against dense and sparse alternatives. The asymptotic distribution of the test statistic under null hypothesis is obtained and the power of the test is analyzed. To avoid the slow convergence rate of the asymptotic distribution, we realize our method by Bootstrap procedures. Simulation studies and the analysis of leukemia dataset are carried out to verify the numerical performance.\",\"PeriodicalId\":51242,\"journal\":{\"name\":\"Brazilian Journal of Probability and Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Brazilian Journal of Probability and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1214/21-bjps519\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Brazilian Journal of Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/21-bjps519","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0

摘要

摘要在对科学数据,特别是生物信息学数据进行统计分析时,经常会出现多变量双样本检验问题。为了检测两个平均向量之间具有不同值的分量,众所周知的程序是应用平方和类型测试,例如Hoteling的T2测试。然而,由于奇异协方差矩阵和累积误差,这种测试不适合高维设置。目前,高维数据的测试方法很多,主要有平方和型和最大型两种。平方和类型测试统计相对于稀疏备选方案的性能较差。并且Max类型检验统计量的功能不足以处理非稀疏数据集。本文提出了一种最大偏和型统计量Neyman截断检验,它是由边际检验统计量的最大偏和进行的。除了非稀疏数据集,Neyman的截断测试对密集和稀疏的替代方案也有很大的优势。得到了零假设下检验统计量的渐近分布,并分析了检验的幂。为了避免渐近分布的收敛速度慢,我们通过Bootstrap程序实现了我们的方法。对白血病数据集进行了仿真研究和分析,验证了数值性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Neyman’s truncation test for two-sample means under high dimensional setting
Abstract. Multivariate two-sample testing problems often arise from the statistical analysis for scientific data, especially for bioinformatics data. To detect components with different values between two mean vectors, well-known procedures are to apply Sum-of-Squares type tests, such as Hotelling’s T 2-test. However, such a test is not suitable to high dimensional settings because of singular covariance matrix and accumulated errors. Nowadays, a lot of test methods for high dimensional data are developed, mainly including two types, Sum-of-Squares type and Max type. The Sum-of-Squares type test statistics have poor performance against sparse alternatives. And the Max type test statistic is not powerful enough to deal with non-sparse datasets. In this paper, we propose a Max-Partial-Sum type statistic named Neyman’s Truncation test, which is conducted by maximum partial sums of marginal test statistics. Besides non-sparse datasets, Neyman’s Truncation test also has great power against dense and sparse alternatives. The asymptotic distribution of the test statistic under null hypothesis is obtained and the power of the test is analyzed. To avoid the slow convergence rate of the asymptotic distribution, we realize our method by Bootstrap procedures. Simulation studies and the analysis of leukemia dataset are carried out to verify the numerical performance.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信