Aggregating Dependent Signals with Heavy-Tailed Combination Tests

Understand

Combining dependent p-values poses a long-standing challenge in statistical inference, particularly when aggregating findings from multiple methods to enhance signal detection.

• Recently, p-value combination tests based on regularly varying-tailed distributions, such as the Cauchy combination test and harmonic mean p-value, have attracted attention for their robustness to unknown dependence.
• This paper provides a theoretical and empirical evaluation of these methods under an asymptotic regime where the number of p-values is fixed and the global test significance level approaches zero.
• We examine two types of dependence among the p-values.