{"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}
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.