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 Royʹs union–intersection principle. Depending on the structure of covariance matrices V 1 and V 2 , three different situations are considered: case (I): V i = σ 2 V 0 i for known V 0 i and an unknown common σ 2 , case (II): V i = σ i 2 V 0 i for known V 0 i and unknown σ 1 2 ≠ σ 2 2 , and case (III): completely unknown V i . 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.