The generalized P-value in one-sided testing in two sample multivariate normal populations

In this paper we develop a new test procedure for the one-sided testing problem in two sample multivariate normal populations, i.e., whether one mean vector dominates the other. The main idea of the proposed test relies on a combination of the generalized P-value and Roy's union–intersection principle. Depending on the structure of covariance matrices V1V1 and V2V2, three different situations are considered: case (I): Vi=σ2V0iVi=σ2V0i for known V0iV0i and an unknown common σ2σ2, case (II): Vi=σi2V0i for known V0iV0i and unknown σ12≠σ22, and case (III): completely unknown ViVi. We calculate the generalized P-value using a resampling technique and compare with the existing methods via numerical studies. We show that our proposed tests based on the generalized P-value control the nominal size and achieve more power than some existing test procedures.