Two-Sample Thresholding Tests for High-Dimensional Means

• Activity Number: 332
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Jun Li*+ and Song Xi Chen and Ping-Shou Zhong
• Companies: Kent State University and Iowa State University/Peking University and Michigan State University
• Keywords: high dimensional data ; test ; large deviation

Abstract

We propose two tests for the equality of two population mean vectors under high dimensionality and column-wise dependence by thresholding. They are designed to obtain better power performance when the mean vectors of two populations differ only in a small number of coordinates. The first test is constructed based on the original data and achieves a power improvement by reducing the level of variance of the test statistics with thresholding. When the data are column-wise dependent, the second test based on transformed data by the inverse of the linear combination of two covariance matrices produces further power improvement by not only reducing the variance but also enhancing the signal strength. The asymptotic distributions of test statistics are established and the power of two tests are analyzed. It is shown that the second test is particularly powerful by incorporating the correlations among the coordinates of the variables. Simulation studies are conducted to confirm the theoretical findings and to offer practical performance of the tests.