An RIHT statistic for testing the equality of several high-dimensional mean vectors under homoskedasticity

Abstract

In this article, the problem of testing the equality of several mean vectors is considered under the homoskedasticity in a high-dimensional setting. A ridgelized Hotelling's T2 test (RIHT) is developed and the asymptotic distributions are derived. By requiring only the conditions on the first four moments of the underlying distribution, the RIHT test can be used to test the mean vector free of population distributions under both p≥n and p<n and improve the power of the classic Hotelling's T2 test. The innovations of the proposed statistic include the following: (1) the RIHT statistic is derived in accordance with a penalized likelihood ratio test; (2) the exact four-moment theorem of the RIHT test makes it possible to test data with an arbitrary distribution; and (3) the proposed statistic is less sensitive to highly correlated data from simulations due to the penalty imposed on concentration matrix. Simulations and real data applications show that the RIHT test performs well and is more powerful than alternatives.