A minimum Wasserstein distance approach to Fisher's combination of independent discrete p-values
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916790809919488 |
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| author | Contador, Gonzalo Wu, Zheyang |
| author_facet | Contador, Gonzalo Wu, Zheyang |
| contents | This paper introduces a comprehensive framework to adjust a discrete test statistic for improving its hypothesis testing procedure. The adjustment minimizes the Wasserstein distance to a null-approximating continuous distribution, tackling some fundamental challenges inherent in combining statistical significances derived from discrete distributions. The related theory justifies Lancaster's mid-p and mean-value chi-squared statistics for Fisher's combination as special cases. However, in order to counter the conservative nature of Lancaster's testing procedures, we propose an updated null-approximating distribution. It is achieved by further minimizing the Wasserstein distance to the adjusted statistics within a proper distribution family. Specifically, in the context of Fisher's combination, we propose an optimal gamma distribution as a substitute for the traditionally used chi-squared distribution. This new approach yields an asymptotically consistent test that significantly improves type I error control and enhances statistical power. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_07692 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A minimum Wasserstein distance approach to Fisher's combination of independent discrete p-values Contador, Gonzalo Wu, Zheyang Statistics Theory Methodology 62E17, 62G10, 60E07 This paper introduces a comprehensive framework to adjust a discrete test statistic for improving its hypothesis testing procedure. The adjustment minimizes the Wasserstein distance to a null-approximating continuous distribution, tackling some fundamental challenges inherent in combining statistical significances derived from discrete distributions. The related theory justifies Lancaster's mid-p and mean-value chi-squared statistics for Fisher's combination as special cases. However, in order to counter the conservative nature of Lancaster's testing procedures, we propose an updated null-approximating distribution. It is achieved by further minimizing the Wasserstein distance to the adjusted statistics within a proper distribution family. Specifically, in the context of Fisher's combination, we propose an optimal gamma distribution as a substitute for the traditionally used chi-squared distribution. This new approach yields an asymptotically consistent test that significantly improves type I error control and enhances statistical power. |
| title | A minimum Wasserstein distance approach to Fisher's combination of independent discrete p-values |
| topic | Statistics Theory Methodology 62E17, 62G10, 60E07 |
| url | https://arxiv.org/abs/2309.07692 |