A sequential rejection testing method for high-dimensional regression with correlated variables

TL;DR

This paper introduces a modular sequential rejection testing method for high-dimensional linear models that effectively detects groups of correlated variables while controlling the familywise error rate, improving power over traditional methods.

Contribution

It presents a novel hierarchical inference approach using repeated sample splitting and sequential rejection, specifically addressing correlated variables in high-dimensional settings.

Findings

Asymptotic control of familywise error rate achieved

Improved power over standard non-sequential methods

Validated with simulated and real data

Abstract

We propose a general, modular method for significance testing of groups (or clusters) of variables in a high-dimensional linear model. In presence of high correlations among the covariables, due to serious problems of identifiability, it is indispensable to focus on detecting groups of variables rather than singletons. We propose an inference method which allows to build in hierarchical structures. It relies on repeated sample splitting and sequential rejection, and we prove that it asymptotically controls the familywise error rate. It can be implemented on any collection of clusters and leads to improved power in comparison to more standard non-sequential rejection methods. We complete the theoretical analysis with empirical results for simulated and real data.