A simultaneous test of mean vector and covariance matrix in high-dimensional settings

Abstract In this paper, the problem of simultaneously testing mean vector and covariance matrix of one-sample population is investigated in high-dimensional settings. We propose a new test statistic and obtain its asymptotic distributions under null and local alternative hypotheses, respectively. Our asymptotic result for proposed test does not need some conditions such as linearity between the sample size and dimension used in existing studies. Simulation results also demonstrate our new test not only can control reasonably the nominal level but also has greater empirical powers than competing tests.