On testing mean of high dimensional compositional data
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910407548993536 |
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| author | Jiang, Qianqian Li, Wenbo Li, Zeng |
| author_facet | Jiang, Qianqian Li, Wenbo Li, Zeng |
| contents | We investigate one/two-sample mean tests for high-dimensional compositional data when the number of variables is comparable with the sample size, as commonly encountered in microbiome research. Existing methods mainly focus on max-type test statistics which are suitable for detecting sparse signals. However, in this paper, we introduce a novel approach using sum-type test statistics which are capable of detecting weak but dense signals. By establishing the asymptotic independence between the max-type and sum-type test statistics, we further propose a combined max-sum type test to cover both cases. We derived the asymptotic null distributions and power functions for these test statistics. Simulation studies demonstrate the superiority of our max-sum type test statistics which exhibit robust performance regardless of data sparsity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08355 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On testing mean of high dimensional compositional data Jiang, Qianqian Li, Wenbo Li, Zeng Statistics Theory We investigate one/two-sample mean tests for high-dimensional compositional data when the number of variables is comparable with the sample size, as commonly encountered in microbiome research. Existing methods mainly focus on max-type test statistics which are suitable for detecting sparse signals. However, in this paper, we introduce a novel approach using sum-type test statistics which are capable of detecting weak but dense signals. By establishing the asymptotic independence between the max-type and sum-type test statistics, we further propose a combined max-sum type test to cover both cases. We derived the asymptotic null distributions and power functions for these test statistics. Simulation studies demonstrate the superiority of our max-sum type test statistics which exhibit robust performance regardless of data sparsity. |
| title | On testing mean of high dimensional compositional data |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2404.08355 |