Preprint: Validity and Power of Heavy-Tailed Combination Tests under Asymptotic Dependence

A new preprint on Arxiv, Validity and Power of Heavy-Tailed Combination Tests under Asymptotic Dependence, develops a unified theoretical framework for understanding the behavior of heavy-tailed p-value combination methods under broad dependence structures:

👉 arXiv:2508.05818

Using multivariate regularly varying copulas to characterize joint lower-tail behavior, the paper shows:

• Heavy-tailed combination tests remain asymptotically valid when p-values have multivariate regularly varying copulas the transformation distribution has tail index ( \gamma \le 1 ).
• The choice ( \gamma = 1 ) maximizes power while preserving validity.
• Bonferroni emerges as the limiting ( \gamma \to 0 ) case and becomes overly conservative under asymptotic dependence.
• Heavy-tailed tests with ( \gamma = 1 ) (e.g., truncated Cauchy or Pareto combinations) achieve increasing asymptotic power gains as lower-tail dependence strengthens.

The framework provides theoretical support for using heavy-tailed combination tests to enhance power while controlling false positives under complex dependence.