  We consider testing for two-sample means of high dimensional populations by
thresholding. Two tests are investigated, which are designed for better power
performance when the two population mean vectors differ only in sparsely
populated coordinates. The first test is constructed by carrying out
thresholding to remove the non-signal bearing dimensions. The second test
combines data transformation via the precision matrix with the thresholding.
The benefits of the thresholding and the data transformations are showed by a
reduced variance of the test thresholding statistics, the improved power and a
wider detection region of the tests. Simulation experiments and an empirical
study are performed to confirm the theoretical findings and to demonstrate the
practical implementations.
