A Heavily Right Strategy for Statistical Inference with Dependent Studies in Any Dimension
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arXiv
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| Format: | Preprint |
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2025
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| author | Liu, Tianle Meng, Xiao-Li Pillai, Natesh S. |
| author_facet | Liu, Tianle Meng, Xiao-Li Pillai, Natesh S. |
| contents | We leverage recent advances in heavy-tail approximations for global hypothesis testing with dependent studies to construct approximate confidence regions without modeling or estimating their dependence structures. A non-rejection region is a confidence region but it may not be convex. Convexity is appealing because it ensures any one-dimensional linear projection of the region is a confidence interval, easy to compute and interpret. We show why convexity fails for nearly all heavy-tail combination tests proposed in recent years, including the influential Cauchy combination test. These insights motivate a \textit{heavily right} strategy: truncating the left half of the Cauchy distribution to obtain the Half-Cauchy combination test. The harmonic mean test also corresponds to a heavily right distribution with a Cauchy-like tail, namely a Pareto distribution with unit power. We prove that both approaches guarantee convexity when individual studies are summarized by Hotelling $T^2$ or $χ^{2}$ statistics (regardless of the validity of this summary) and provide efficient, \textit{exact} algorithms for implementation. Applying these methods, we develop a divide-and-combine strategy for mean estimation in any dimension and construct simultaneous confidence intervals in a network meta-analysis for treatment effect comparisons across multiple clinical trials. We also present many open problems and conclude with epistemic reflections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01065 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Heavily Right Strategy for Statistical Inference with Dependent Studies in Any Dimension Liu, Tianle Meng, Xiao-Li Pillai, Natesh S. Methodology Statistics Theory We leverage recent advances in heavy-tail approximations for global hypothesis testing with dependent studies to construct approximate confidence regions without modeling or estimating their dependence structures. A non-rejection region is a confidence region but it may not be convex. Convexity is appealing because it ensures any one-dimensional linear projection of the region is a confidence interval, easy to compute and interpret. We show why convexity fails for nearly all heavy-tail combination tests proposed in recent years, including the influential Cauchy combination test. These insights motivate a \textit{heavily right} strategy: truncating the left half of the Cauchy distribution to obtain the Half-Cauchy combination test. The harmonic mean test also corresponds to a heavily right distribution with a Cauchy-like tail, namely a Pareto distribution with unit power. We prove that both approaches guarantee convexity when individual studies are summarized by Hotelling $T^2$ or $χ^{2}$ statistics (regardless of the validity of this summary) and provide efficient, \textit{exact} algorithms for implementation. Applying these methods, we develop a divide-and-combine strategy for mean estimation in any dimension and construct simultaneous confidence intervals in a network meta-analysis for treatment effect comparisons across multiple clinical trials. We also present many open problems and conclude with epistemic reflections. |
| title | A Heavily Right Strategy for Statistical Inference with Dependent Studies in Any Dimension |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2501.01065 |