Validity and Power of Heavy-Tailed Combination Tests under Asymptotic Dependence
Bibliographic record
Abstract
Heavy-tailed combination tests, such as the Cauchy combination test and harmonic mean p-value method, are widely used for testing global null hypotheses by aggregating dependent p-values. Existing theoretical guarantees, however, are largely restricted to the case of asymptotically independent p-values, leaving the behavior of these tests under broader dependence structures poorly understood. We develop a unified framework based on multivariate regularly varying copulas, a flexible class defined by a mild regularity condition on the joint behavior of p-values near zero, that accommodates a wide range of dependence structures. Within this framework, heavy-tailed combination tests are asymptotically valid when the transformation distribution has tail index $γ\leq 1$, with $γ= 1$ maximizing power while preserving validity. We further show that combination tests with $γ= 1$ achieve strictly greater asymptotic power than Bonferroni's method if and only if the p-values are not asymptotically independent and signals are not extremely sparse, with the power advantage growing as dependence strengthens. Bonferroni emerges as the $γ\to 0$ limit and becomes overly conservative under asymptotic dependence. These results provide theoretical support for using truncated Cauchy or Pareto combination tests, offering a principled approach to enhance power while controlling false positives under complex dependence.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.075 | 0.405 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.011 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".