An Adaptible Generalization of Hotelling's T2 Test in High Dimension

• Activity Number: 662
• Type: Contributed
• Date/Time: Thursday, August 4, 2016 : 8:30 AM to 10:20 AM
• Sponsor: SSC
• Author(s): Haoran Li* and Debashis Paul and Alex Aue and Jie Peng and Pei Wang
• Companies: and University of California at Davis and University of California at Davis and University of California at Davis and Icahn School of Medicine at Mount Sinai
• Keywords: High dimensional test ; Hypothesis testing ; Random matrix ; Hotelling's T2 ; Regularization

Abstract

A test is proposed for the two-sample testing problem of testing equality of mean vectors in the high dimensional setting. The test is based on a specific generalization of the idea of a ridge-regularized Hotelling's T2 first studied in the one-sample case by Chen et al. (2011). The cut-off values for the test are determined through asymptotic theory, but several finite-sample modifications are suggested. The proposed test has excellent practical performance for a wide range of parameter settings and is also quite robust to distributional assumptions as predicted by the theory. Through an extensive simulation study, the test is shown to compare favorably against a host of competitors designed to tackle high-dimensional testing problems. Although the test is established under Gaussianity of observations, it's shown to be quite insensitive to this assumption.