2025/01/02 by Tianle Liu, Xiao-Li Meng, Liu, Tianle +3 · 1 citation
Decision Sciences · #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Scientific Computing and Data Management #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2501.01065
openalex publication_date 2025/01/02 · openalex created_date 2025/01/04 · openalex updated_date 2026/07/29
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 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 T2 or χ2 statistics (regardless of the validity of this summary) and provide efficient, 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.