Test of the Equality of Several High-Dimensional Covariance Matrices: A Normal-Reference Approach
As the field of big data continues to evolve, there is an increasing necessity to evaluate the equality of multiple high-dimensional covariance matrices. Many existing methods rely on approximations to the null distribution of the test statistic or its extreme-value distributions under stringent con...
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| author | Jingyi Wang Tianming Zhu Jin-Ting Zhang |
| author_facet | Jingyi Wang Tianming Zhu Jin-Ting Zhang |
| author_sort | Jingyi Wang |
| collection | DOAJ |
| description | As the field of big data continues to evolve, there is an increasing necessity to evaluate the equality of multiple high-dimensional covariance matrices. Many existing methods rely on approximations to the null distribution of the test statistic or its extreme-value distributions under stringent conditions, leading to outcomes that are either overly permissive or excessively cautious. Consequently, these methods often lack robustness when applied to real-world data, as verifying the required assumptions can be arduous. In response to these challenges, we introduce a novel test statistic utilizing the normal-reference approach. We demonstrate that the null distribution of this test statistic shares the same limiting distribution as a chi-square-type mixture under certain regularity conditions, with the latter reliably estimable from data using the three-cumulant matched chi-square-approximation. Additionally, we establish the asymptotic power of our proposed test. Through comprehensive simulation studies and real data analysis, our proposed test demonstrates superior performance in terms of size control compared to several competing methods. |
| format | Article |
| id | doaj-art-16d297a5fee64802b7b8ab55338500c4 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-16d297a5fee64802b7b8ab55338500c42025-01-24T13:40:04ZengMDPI AGMathematics2227-73902025-01-0113229510.3390/math13020295Test of the Equality of Several High-Dimensional Covariance Matrices: A Normal-Reference ApproachJingyi Wang0Tianming Zhu1Jin-Ting Zhang2Department of Statistics and Data Science, National University of Singapore, Singapore 117546, SingaporeNational Institute of Education, Nanyang Technological University, Singapore 637616, SingaporeDepartment of Statistics and Data Science, National University of Singapore, Singapore 117546, SingaporeAs the field of big data continues to evolve, there is an increasing necessity to evaluate the equality of multiple high-dimensional covariance matrices. Many existing methods rely on approximations to the null distribution of the test statistic or its extreme-value distributions under stringent conditions, leading to outcomes that are either overly permissive or excessively cautious. Consequently, these methods often lack robustness when applied to real-world data, as verifying the required assumptions can be arduous. In response to these challenges, we introduce a novel test statistic utilizing the normal-reference approach. We demonstrate that the null distribution of this test statistic shares the same limiting distribution as a chi-square-type mixture under certain regularity conditions, with the latter reliably estimable from data using the three-cumulant matched chi-square-approximation. Additionally, we establish the asymptotic power of our proposed test. Through comprehensive simulation studies and real data analysis, our proposed test demonstrates superior performance in terms of size control compared to several competing methods.https://www.mdpi.com/2227-7390/13/2/295k-sample equal-covariance matrix testingchi-square-type mixtureshigh-dimensional datathree-cumulant matched chi-square-approximation |
| spellingShingle | Jingyi Wang Tianming Zhu Jin-Ting Zhang Test of the Equality of Several High-Dimensional Covariance Matrices: A Normal-Reference Approach Mathematics k-sample equal-covariance matrix testing chi-square-type mixtures high-dimensional data three-cumulant matched chi-square-approximation |
| title | Test of the Equality of Several High-Dimensional Covariance Matrices: A Normal-Reference Approach |
| title_full | Test of the Equality of Several High-Dimensional Covariance Matrices: A Normal-Reference Approach |
| title_fullStr | Test of the Equality of Several High-Dimensional Covariance Matrices: A Normal-Reference Approach |
| title_full_unstemmed | Test of the Equality of Several High-Dimensional Covariance Matrices: A Normal-Reference Approach |
| title_short | Test of the Equality of Several High-Dimensional Covariance Matrices: A Normal-Reference Approach |
| title_sort | test of the equality of several high dimensional covariance matrices a normal reference approach |
| topic | k-sample equal-covariance matrix testing chi-square-type mixtures high-dimensional data three-cumulant matched chi-square-approximation |
| url | https://www.mdpi.com/2227-7390/13/2/295 |
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