{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T07:15:30Z","timestamp":1766733330776,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T00:00:00Z","timestamp":1666569600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"UIC New Faculty Start-up Research Fund","award":["R72021106","2022B1212010006"],"award-info":[{"award-number":["R72021106","2022B1212010006"]}]},{"name":"Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College (UIC)","award":["R72021106","2022B1212010006"],"award-info":[{"award-number":["R72021106","2022B1212010006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Testing multivariate normality is an ever-lasting interest in the goodness-of-fit area since the classical Pearson\u2019s chi-squared test. Among the numerous approaches in the construction of tests for multivariate normality, normal characterization is one of the common approaches, which can be divided into the necessary and sufficient characterization and necessary-only characterization. We construct a test for multivariate normality by combining the necessary-only characterization and the idea of statistical representative points in this paper. The main idea is to transform a high-dimensional sample into a one-dimensional one through the necessary normal characterization and then employ the representative-point-based Pearson\u2019s chi-squared test. A limited Monte Carlo study shows a considerable power improvement of the representative-point-based chi-square test over the traditional one. An illustrative example is given to show the supplemental function of the new test when used together with existing ones in the literature.<\/jats:p>","DOI":"10.3390\/axioms11110587","type":"journal-article","created":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T10:09:23Z","timestamp":1666606163000},"page":"587","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Testing Multivariate Normality Based on t-Representative Points"],"prefix":"10.3390","volume":"11","author":[{"given":"Jiajuan","family":"Liang","sequence":"first","affiliation":[{"name":"Department of Statistics and Data Science, BNU-HKBU United International College, Zhuhai 519087, China"},{"name":"Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College, Zhuhai 519087, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ping","family":"He","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, BNU-HKBU United International College, Zhuhai 519087, China"},{"name":"Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College, Zhuhai 519087, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, BNU-HKBU United International College, Zhuhai 519087, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1214\/aoms\/1177693441","article-title":"A characterization of the multivariate normal distribution","volume":"42","author":"Anderson","year":"1971","journal-title":"Ann. 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