Many-sample tests for the equality and the proportionality hypotheses between large covariance matrices
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912020860764160 |
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| author | Mei, Tianxing Wang, Chen Yao, Jianfeng |
| author_facet | Mei, Tianxing Wang, Chen Yao, Jianfeng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06296 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Many-sample tests for the equality and the proportionality hypotheses between large covariance matrices Mei, Tianxing Wang, Chen Yao, Jianfeng Statistics Theory Primary 62H15, secondary 62H10 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. |
| title | Many-sample tests for the equality and the proportionality hypotheses between large covariance matrices |
| topic | Statistics Theory Primary 62H15, secondary 62H10 |
| url | https://arxiv.org/abs/2409.06296 |