A Power Study For One-Sided Multivariate Test

Abstract

In this study, parametric and nonparametric tests for two classes of multivariate alternatives called tailored and omnibus alternatives are considered. included among the tests are ump parametric tests and their nonparametric counterparts. from a simulation study it is shown that the proposed tests of tailored altenatives have substantially greater power than the omnibus tests under the tailored alternatives. conditions under which omnibus tests perform well are given. the asymptotic properties of the proposed tailored tests are investigated. for the multivariate case, unlike the univariate case, the are of the wilcoxon statistic relative to the t test depends not only on the population distribution but also on such factors as dimension, covariance structure, and correlation. the robustness of tests of tailored alternatives to misspecification of the form of the tailored alternative is investigated. modest model misspecification has only small effects on efficiencies. small sample test procedures are discussed with the focus being on the situation of a smaller sample size than the number of measurements. permutation tests of one-sided tailored alternatives are considered. the normal approximation to the permutation distribution is shown to be useful even for small sample size. a power study is conducted to investigate factors that affect the relative performances of the proposed test.