大型协方差矩阵之间的相等假设和比例假设的多样本检验

Tianxing Mei, Chen Wang, Jianfeng Yao
{"title":"大型协方差矩阵之间的相等假设和比例假设的多样本检验","authors":"Tianxing Mei, Chen Wang, Jianfeng Yao","doi":"arxiv-2409.06296","DOIUrl":null,"url":null,"abstract":"This paper proposes procedures for testing the equality hypothesis and the\nproportionality hypothesis involving a large number of $q$ covariance matrices\nof dimension $p\\times p$. Under a limiting scheme where $p$, $q$ and the sample\nsizes from the $q$ populations grow to infinity in a proper manner, the\nproposed test statistics are shown to be asymptotically normal. Simulation\nresults show that finite sample properties of the test procedures are\nsatisfactory under both the null and alternatives. As an application, we derive\na test procedure for the Kronecker product covariance specification for\ntransposable data. Empirical analysis of datasets from the Mouse Aging Project\nand the 1000 Genomes Project (phase 3) is also conducted.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"35 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Many-sample tests for the equality and the proportionality hypotheses between large covariance matrices\",\"authors\":\"Tianxing Mei, Chen Wang, Jianfeng Yao\",\"doi\":\"arxiv-2409.06296\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper proposes procedures for testing the equality hypothesis and the\\nproportionality hypothesis involving a large number of $q$ covariance matrices\\nof dimension $p\\\\times p$. Under a limiting scheme where $p$, $q$ and the sample\\nsizes from the $q$ populations grow to infinity in a proper manner, the\\nproposed test statistics are shown to be asymptotically normal. Simulation\\nresults show that finite sample properties of the test procedures are\\nsatisfactory under both the null and alternatives. As an application, we derive\\na test procedure for the Kronecker product covariance specification for\\ntransposable data. Empirical analysis of datasets from the Mouse Aging Project\\nand the 1000 Genomes Project (phase 3) is also conducted.\",\"PeriodicalId\":501379,\"journal\":{\"name\":\"arXiv - STAT - Statistics Theory\",\"volume\":\"35 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - STAT - Statistics Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.06296\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - STAT - Statistics Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06296","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

本文提出了涉及大量维数为 $p/times p$ 的 $q$ 协方差矩阵的相等假设和比例假设检验程序。在一个限制方案下,即 $p$、$q$ 和来自 $q$ 种群的样本量以适当的方式增长到无穷大,所提出的检验统计量被证明是渐近正态的。模拟结果表明,检验程序的有限样本特性在零样本和替代样本下都是令人满意的。作为应用,我们推导出了可传递数据的 Kronecker 乘积协方差规范的检验程序。我们还对小鼠衰老项目和 1000 基因组项目(第 3 阶段)的数据集进行了实证分析。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Many-sample tests for the equality and the proportionality hypotheses between large covariance matrices
This paper proposes procedures for testing the equality hypothesis and the proportionality hypothesis involving a large number of $q$ covariance matrices of dimension $p\times p$. Under a limiting scheme where $p$, $q$ and the sample sizes from the $q$ populations grow to infinity in a proper manner, the proposed test statistics are shown to be asymptotically normal. Simulation results show that finite sample properties of the test procedures are satisfactory under both the null and alternatives. As an application, we derive a test procedure for the Kronecker product covariance specification for transposable data. Empirical analysis of datasets from the Mouse Aging Project and the 1000 Genomes Project (phase 3) is also conducted.
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
自引率
0.00%
发文量
0
×
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