Many-sample tests for the dimensionality hypothesis for large covariance matrices among groups
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910021112037376 |
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| author | Mei, Tianxing Wang, Chen Yao, Jianfeng |
| author_facet | Mei, Tianxing Wang, Chen Yao, Jianfeng |
| contents | In this paper, we consider procedures for testing hypotheses on the dimension of the linear span generated by a growing number of $p\times p$ covariance matrices from independent $q$ populations. Under a proper limiting scheme where all the parameters, $q$, $p$, and the sample sizes from the $q$ populations, are allowed to increase to infinity, we derive the asymptotic normality of the proposed test statistics. The proposed test procedures show satisfactory performance in finite samples under both the null and the alternative. We also apply the proposed many-sample dimensionality test to investigate a matrix-valued gene dataset from the Mouse Aging Project and gain some new knowledge about its covariance structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12653 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Many-sample tests for the dimensionality hypothesis for large covariance matrices among groups Mei, Tianxing Wang, Chen Yao, Jianfeng Statistics Theory 62H15(Primary), 62H10(Secondary) In this paper, we consider procedures for testing hypotheses on the dimension of the linear span generated by a growing number of $p\times p$ covariance matrices from independent $q$ populations. Under a proper limiting scheme where all the parameters, $q$, $p$, and the sample sizes from the $q$ populations, are allowed to increase to infinity, we derive the asymptotic normality of the proposed test statistics. The proposed test procedures show satisfactory performance in finite samples under both the null and the alternative. We also apply the proposed many-sample dimensionality test to investigate a matrix-valued gene dataset from the Mouse Aging Project and gain some new knowledge about its covariance structures. |
| title | Many-sample tests for the dimensionality hypothesis for large covariance matrices among groups |
| topic | Statistics Theory 62H15(Primary), 62H10(Secondary) |
| url | https://arxiv.org/abs/2602.12653 |