A general adaptive framework for multivariate point null testing

TL;DR

This paper introduces a versatile adaptive testing framework for multivariate point null hypotheses that enhances power and can be applied across various problems, including those lacking existing tailored methods.

Contribution

It develops a general, adaptive approach for multivariate hypothesis testing with theoretical guarantees, applicable even when specific tailored methods are unavailable.

Findings

The proposed tests match the performance of tailored methods when they exist.

Simulation results demonstrate improved power over traditional methods.

The framework is adaptable to new testing scenarios without existing solutions.

Abstract

As a common step in refining their scientific inquiry, investigators are often interested in performing some screening of a collection of given statistical hypotheses. For example, they may wish to determine whether any one of several patient characteristics are associated with a health outcome of interest. Existing generic methods for testing a multivariate hypothesis -- such as multiplicity corrections applied to individual hypothesis tests -- can easily be applied across a variety of problems but can suffer from low power in some settings. Tailor-made procedures can attain higher power by building around problem-specific information but typically cannot be easily adapted to novel settings. In this work, we propose a general framework for testing a multivariate point null hypothesis in which the test statistic is adaptively selected to provide increased power. We present theoretical large-sample guarantees for our test under both fixed and local alternatives. In simulation studies, we show that tests created using our framework can perform as well as tailor-made methods when the latter are available, and we illustrate how our procedure can be used to create tests in two settings in which tailor-made methods are not currently available.