Simultaneous inference of correlated marginal tests using intersection-union or union-intersection test principle

TL;DR

This paper compares intersection-union and union-intersection tests for simultaneous inference, highlighting their power and interpretability trade-offs in correlated marginal testing scenarios.

Contribution

It provides a comparative analysis of classical IUT and all-in-alternative UIT methods, emphasizing their performance based on correlation and alternative patterns.

Findings

AiaUIT offers acceptable power loss with simple confidence intervals.

Correlation and alternative patterns influence test power.

UIT provides straightforward interpretation.

Abstract

Two main approaches in simultaneous inference are intersection-union tests and union-intersection tests. For intersection-union hypotheses, the classical IUT based on marginal p-values and the all-in-alternative UIT are compared. Depending on correlation, number of marginal tests and patterns of the alternative the inherent power loss of the aiaUIT seems to be acceptable, considering its advantage, namely the availability of simple-to-interpret simultaneous confidence interval.