In this paper, we study the problem of testing the mean vectors of highdimensional data in both one-sample and two-sample cases. The proposed testingprocedures employ maximum-type statistics and the parametric bootstraptechniques to compute the critical values. Different from the existing teststhat heavily rely on the structural conditions on the unknown covariancematrices, the proposed tests allow general covariance structures of the dataand therefore enjoy wide scope of applicability in practice. To enhance powersof the tests against sparse alternatives, we further propose two-stepprocedures with a preliminary feature screening step. Theoretical properties ofthe proposed tests are investigated. Through extensive numerical experiments onsynthetic datasets and an human acute lymphoblastic leukemia gene expressiondataset, we illustrate the performance of the new tests and how they mayprovide assistance on detecting disease-associated gene-sets. The proposedmethods have been implemented in an R-package HDtest and are available on CRAN.
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