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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.19960 |
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| _version_ | 1866915636641267712 |
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| author | Ghosh, Deepra Sarkar, Sanat K. |
| author_facet | Ghosh, Deepra Sarkar, Sanat K. |
| contents | This paper develops a general framework for controlling the false discovery rate (FDR) in multiple testing of Gaussian means against two-sided alternatives. The widely used Benjamini-Hochberg (BH) procedure provides exact FDR control under independence or conservative control under specific one-sided dependence structures, but its validity for correlated two-sided tests has remained an open question. We introduce the notion of positive left-tail dependence under the null (PLTDN), extending classical dependence assumptions to two-sided settings, and show that it ensures valid FDR control for BH-type procedures. Building on this framework, we propose a family of generalized shifted BH (GSBH) methods that incorporate correlation information through simple p-value adjustments. Simulation results demonstrate reliable FDR control and improved power across a range of dependence structures, while an application to an HIV gene expression dataset illustrates the practical effectiveness of the proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19960 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dependence-Aware False Discovery Rate Control in Two-Sided Gaussian Mean Testing Ghosh, Deepra Sarkar, Sanat K. Methodology Statistics Theory This paper develops a general framework for controlling the false discovery rate (FDR) in multiple testing of Gaussian means against two-sided alternatives. The widely used Benjamini-Hochberg (BH) procedure provides exact FDR control under independence or conservative control under specific one-sided dependence structures, but its validity for correlated two-sided tests has remained an open question. We introduce the notion of positive left-tail dependence under the null (PLTDN), extending classical dependence assumptions to two-sided settings, and show that it ensures valid FDR control for BH-type procedures. Building on this framework, we propose a family of generalized shifted BH (GSBH) methods that incorporate correlation information through simple p-value adjustments. Simulation results demonstrate reliable FDR control and improved power across a range of dependence structures, while an application to an HIV gene expression dataset illustrates the practical effectiveness of the proposed approach. |
| title | Dependence-Aware False Discovery Rate Control in Two-Sided Gaussian Mean Testing |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2511.19960 |