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Aggregating Dependent Signals with Heavy-Tailed Combination Tests

Abstract Number:

1511 

Submission Type:

Contributed Abstract 

Contributed Abstract Type:

Paper 

Participants:

Lin Gui (1), Yuchao Jiang (2), Jingshu Wang (1)

Institutions:

(1) N/A, N/A, (2) Texas A&M University, N/A

Co-Author(s):

Yuchao Jiang  
Texas A&M University
Jingshu Wang  
N/A

First Author:

Lin Gui  
N/A

Presenting Author:

Lin Gui  
N/A

Abstract Text:

Combining dependent p-values presents a longstanding challenge in statistical inference, particularly when aggregating results from various methods to enhance signal detection. Recent developments in p-value combination tests through transformations based on regularly varying tailed distributions, such as the Cauchy combination test and harmonic mean p-value, have gained significant interest for their effectiveness in managing unknown p-value dependencies. This paper provides a theoretical and empirical evaluation of these methods within an asymptotic framework, where the number of dependent p-values is fixed and the global test significance level approaches zero. Our findings show that while these combination tests are asymptotically valid for pairwise quasi-asymptotically independent test statistics, e.g., bivariate normal variables with no perfect correlation, they are also asymptotically equivalent to the Bonferroni test under the same asymptotic regime. Empirical results indicate that the power advantage of combination tests over the Bonferroni test diminishes under quasi-asymptotic independence of test statistics but that the combination tests exhibit substantial

Keywords:

Cauchy combination test|Dependent p-values combination|Quasi-asymptotic independence| t-copula| |

Sponsors:

IMS

Tracks:

Statistical Theory

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