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Aggregating dependent signals with heavy-tailed combination tests.

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Summary
This summary is machine-generated.

Combining p-values from multiple statistical tests is challenging. New methods using Cauchy and harmonic means show promise for dependent p-values, offering power gains over traditional tests in certain scenarios.

Keywords:
Cauchy combination testDependent p-value combinationHarmonic mean p-valueQuasi-asymptotic independencet copula

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Area of Science:

  • Statistical inference
  • Dependence modeling
  • Hypothesis testing

Background:

  • Combining dependent p-values is a significant challenge in statistical inference.
  • Methods like Cauchy and harmonic mean p-value combination are gaining attention for their robustness to unknown dependence.
  • Evaluating these methods under asymptotic regimes is crucial for understanding their behavior.

Purpose of the Study:

  • To theoretically and empirically evaluate Cauchy and harmonic mean p-value combination tests.
  • To investigate the performance of these tests under different types of p-value dependence.
  • To compare their validity and power against the Bonferroni test as significance levels approach zero.

Main Methods:

  • Asymptotic analysis of p-value combination tests.
  • Examination of pairwise asymptotically independent and quasi-asymptotically dependent p-values.
  • Monte Carlo simulations to assess test validity and power.
  • Analysis of test performance based on distribution support and tail heaviness.

Main Results:

  • Under pairwise asymptotic independence, combination tests are asymptotically valid but converge to the Bonferroni test as significance levels decrease.
  • Under pairwise quasi-asymptotic dependence, simulations indicate these tests remain valid and offer power advantages over the Bonferroni test.
  • Test performance is influenced by the support and tail heaviness of the underlying distributions.

Conclusions:

  • Cauchy and harmonic mean p-value combination tests show potential, especially when p-values exhibit substantial dependence.
  • These methods can outperform the Bonferroni test in specific dependent scenarios.
  • Further investigation into distribution properties is warranted for optimal test selection.