Stable combination tests

TL;DR

This paper introduces a stable combination test that extends Cauchy combination tests, offering a simple, reliable, and powerful method for combining multiple tests, effective even with dependent tests, supported by theoretical and empirical evidence.

Contribution

It presents a new stable combination test that generalizes Cauchy tests, maintaining simplicity, good size control, and asymptotic optimality under dependence.

Findings

The stable combination test is computationally simple.

It maintains good size and power properties.

It performs well in finite sample scenarios.

Abstract

This paper proposes a stable combination test, which is a natural extension of Cauchy combination tests by Liu and Xie (2020). Similarly to the Cauchy combination test, our stable combination test is simple to compute, enjoys good sizes, and has asymptotically optimal powers even when the individual tests are not independent. This finding is supported both in theory and in finite samples.