Test for high-dimensional mean vectors via the weighted $L_2$-norm
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914660685447168 |
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| author | Li, Jianghao Niu, Zhenzhen Hong, Shizhe Bai, Zhidong |
| author_facet | Li, Jianghao Niu, Zhenzhen Hong, Shizhe Bai, Zhidong |
| contents | In this paper, we propose a novel approach to test the equality of high-dimensional mean vectors of several populations via the weighted $L_2$-norm. We establish the asymptotic normality of the test statistics under the null hypothesis. We also explain theoretically why our test statistics can be highly useful in weakly dense cases when the nonzero signal in mean vectors is present. Furthermore, we compare the proposed test with existing tests using simulation results, demonstrating that the weighted $L_2$-norm-based test statistic exhibits favorable properties in terms of both size and power. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17143 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Test for high-dimensional mean vectors via the weighted $L_2$-norm Li, Jianghao Niu, Zhenzhen Hong, Shizhe Bai, Zhidong Statistics Theory Methodology In this paper, we propose a novel approach to test the equality of high-dimensional mean vectors of several populations via the weighted $L_2$-norm. We establish the asymptotic normality of the test statistics under the null hypothesis. We also explain theoretically why our test statistics can be highly useful in weakly dense cases when the nonzero signal in mean vectors is present. Furthermore, we compare the proposed test with existing tests using simulation results, demonstrating that the weighted $L_2$-norm-based test statistic exhibits favorable properties in terms of both size and power. |
| title | Test for high-dimensional mean vectors via the weighted $L_2$-norm |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2401.17143 |