{"title":"Testing hypotheses about correlation matrices in general MANOVA designs","authors":"Paavo Sattler, Markus Pauly","doi":"10.1007/s11749-023-00906-6","DOIUrl":null,"url":null,"abstract":"<p>Correlation matrices are an essential tool for investigating the dependency structures of random vectors or comparing them. We introduce an approach for testing a variety of null hypotheses that can be formulated based upon the correlation matrix. Examples cover MANOVA-type hypothesis of equal correlation matrices as well as testing for special correlation structures such as sphericity. Apart from existing fourth moments, our approach requires no other assumptions, allowing applications in various settings. To improve the small sample performance, a bootstrap technique is proposed and theoretically justified. Based on this, we also present a procedure to simultaneously test the hypotheses of equal correlation and equal covariance matrices. The performance of all new test statistics is compared with existing procedures through extensive simulations.\n</p>","PeriodicalId":51189,"journal":{"name":"Test","volume":"37 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Test","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11749-023-00906-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Correlation matrices are an essential tool for investigating the dependency structures of random vectors or comparing them. We introduce an approach for testing a variety of null hypotheses that can be formulated based upon the correlation matrix. Examples cover MANOVA-type hypothesis of equal correlation matrices as well as testing for special correlation structures such as sphericity. Apart from existing fourth moments, our approach requires no other assumptions, allowing applications in various settings. To improve the small sample performance, a bootstrap technique is proposed and theoretically justified. Based on this, we also present a procedure to simultaneously test the hypotheses of equal correlation and equal covariance matrices. The performance of all new test statistics is compared with existing procedures through extensive simulations.
期刊介绍：
TEST is an international journal of Statistics and Probability, sponsored by the Spanish Society of Statistics and Operations Research. English is the official language of the journal.
The emphasis of TEST is placed on papers containing original theoretical contributions of direct or potential value in applications. In this respect, the methodological contents are considered to be crucial for the papers published in TEST, but the practical implications of the methodological aspects are also relevant. Original sound manuscripts on either well-established or emerging areas in the scope of the journal are welcome.
One volume is published annually in four issues. In addition to the regular contributions, each issue of TEST contains an invited paper from a world-wide recognized outstanding statistician on an up-to-date challenging topic, including discussions.
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