Testing High Dimensional Mean Under Sparsity

TL;DR

This paper introduces a new maximum sum-of-squares test for high-dimensional mean vectors that accounts for variable dependence, offering improved power and computational efficiency over existing methods.

Contribution

The paper develops a novel test statistic for high-dimensional mean testing that incorporates variable dependence and extends to two-sample problems without equal covariance assumptions.

Findings

The proposed test outperforms some existing methods in power.

Simulation results validate the test's accuracy under null and alternative hypotheses.

The method is computationally efficient and adaptable to two-sample scenarios.

Abstract

Motivated by the likelihood ratio test under the Gaussian assumption, we develop a maximum sum-of-squares test for conducting hypothesis testing on high dimensional mean vector. The proposed test which incorporates the dependence among the variables is designed to ease the computational burden and to maximize the asymptotic power in the likelihood ratio test. A simulation-based approach is developed to approximate the sampling distribution of the test statistic. The validity of the testing procedure is justified under both the null and alternative hypotheses. We further extend the main results to the two sample problem without the equal covariance assumption. Numerical results suggest that the proposed test can be more powerful than some existing alternatives.