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

• Activity Number: 193
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Wen Zhou* and Jinyuan Chang and Wenxin Zhou
• Companies: Colorado State University and The University of Melbourne and The University of Melbourne
• Keywords: High-dimensional test ; Gaussian approximation ; Testing equality of mean vectors ; Feature screening ; Covariance heterogeneity

Abstract

In this paper, we introduce a fast-computational simulation-based testing procedure that allows for general covariance heterogeneity in the data for both one-sample and two-sample problems. The proposed procedure is based on the maximum-type statistics and the critical values are computed via the Gaussian approximation. Different from most existing tests that rely on certain structural restrictions on the covariance matrix, our method imposes no assumptions on the dependence structure of underlying distributions, which makes it can be easily applied in practice. Theoretical properties for the proposed testing procedure are systematically analyzed, including the rate of convergence, the asymptotic size and power. When testing against sparse alternatives, we develop a preliminary screening step to improve the power of the proposed tests and a data-driven procedure is also developed for practical implementations. Simulation studies demonstrate that, compared to existing methods, our testing procedure provides good performance against strong heterogeneity in the covariance structure of the data.