Two-Sample Tests for High Dimensional Means with Thresholding and Data Transformation

We study two tests for the equality of two population mean vectors under high dimensionality and column-wise dependence by thresholding. They are designed for better power performance when the mean vectors of two populations differ only in sparsely populated coordinates. The first test is constructed by carrying out thresholding to remove those no-signal bearing dimensions. The second test combines data transformation and thresholding by first transforming the data with the precision matrix followed by thresholding. The benefits of the threshodling and the data transformations are demonstrated in terms of reduced variance of the test statistics and the improved power of the tests. Numerical analyses and empirical study are performed to confirm the theoretical findings and to demonstrate the practical implementations.