Simulation-Based Hypothesis Testing of High Dimensional Means Under Covariance Heterogeneity

TL;DR

This paper introduces new simulation-based tests for high-dimensional mean vectors that accommodate general covariance structures, improving power against sparse alternatives, with practical applications in gene expression analysis.

Contribution

It proposes flexible, bootstrap-based testing procedures for high-dimensional means under covariance heterogeneity, including two-step screening methods for enhanced power.

Findings

The tests perform well on synthetic data.

They effectively detect disease-related gene-sets.

The methods are implemented in the R-package HDtest.

Abstract

In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to compute the critical values. Different from the existing tests that heavily rely on the structural conditions on the unknown covariance matrices, the proposed tests allow general covariance structures of the data and therefore enjoy wide scope of applicability in practice. To enhance powers of the tests against sparse alternatives, we further propose two-step procedures with a preliminary feature screening step. Theoretical properties of the proposed tests are investigated. Through extensive numerical experiments on synthetic datasets and an human acute lymphoblastic leukemia gene expression dataset, we illustrate the performance of the new tests and how they may provide assistance on detecting disease-associated gene-sets. The proposed methods have been implemented in an R-package HDtest and are available on CRAN.