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Activity Number: 349 - Contributed Poster Presentations: Section on Statistical Graphics
Type: Contributed
Date/Time: Tuesday, August 9, 2022 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Graphics
Abstract #323684
Title: Unifying Additive P-Value Combination Tests with Regularly Varying Tails
Author(s): Xing Ling* and Yeonwoo Rho and Sangyoon J. Han
Companies: Michigan Technological University and Michigan Technological University and Michigan Technological University
Keywords: Additive combination test; hypothesis testing; multiplicity; regularly varying; stable distribution

This paper proposes a unifying framework to additive $p$-value combination methods such as the harmonic mean $p$ and the Cauchy combination test. These methods can be understood as convex combinations of transformed $p$-values, with a normalizing factor. We prove that the tails of combined statistics can be approximated by stable distributions, as long as the transformation functions are regularly varying. The asymptotic behaviors of tests in this class depend mainly on the variation exponents of their transformation functions. These tests are proven to have asymptotic optimal powers. The finite sample performances are demonstrated with discussion on choices of stability parameter and transformation function. An application to biomedical engineering data is also presented.

Authors who are presenting talks have a * after their name.

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