The Covering Principle: A New Approach to Address Multiplicity in Hypotheses Testing

TL;DR

This paper introduces the covering principle, a novel approach for multiple hypotheses testing that focuses on rejection region coverage, offering strong control of familywise error rate and applications to gate-keeping problems.

Contribution

The paper proposes the covering principle, a new method based on rejection region coverage, expanding the toolkit for multiple testing procedures beyond traditional partitioning principles.

Findings

Strong familywise error rate control achieved

Applicable to general gate-keeping problems

Demonstrates effectiveness through theoretical proofs

Abstract

The closure and the partitioning principles have been used to build various multiple testing procedures in the past three decades. The essence of these two principles is based on parameter space partitioning. In this article, we propose a novel approach coined the covering principle from the perspective of rejection region coverage in the sample space. The covering principle divides the whole family of null hypotheses into a few overlapped sub-families when there is a priority of making decisions for hypothesis testing. We have proven that the multiple testing procedure constructed by the covering principle strongly controls the familywise error rate as long as the multiple tests for each sub-familiy strongly control the type I error. We have illustrated the covering principle can be applied to solve the general gate-keeping problems.