A Class of Rank Order Tests for a General Linear Hypothesis

For a general multivariate linear hypothesis testing problem, a class of permutationally (conditionally) distribution-free tests is proposed and studied. The asymptotic distribution theory of the proposed class of test statistics is studied along with a generalization of the elegant results of Hajek (1968) to the multistatistics and multivariate situations. Asymptotic power and optimality of the proposed tests are established and a characterization of the multivariate multisample location problem [cf. Puri and Sen (1966)] in terms of the proposed linear hypothesis is also considered.