A new permutation test statistic for K-sample multivariate designs

摘要

We consider permutation tests based on a likelihood ratio like statistic for the one way or k-sample design where the observations are l-dimensional vectors. This generalizes both the univariate k-sample case and the two sample multivariate case used in the examples of Kolassa and Robinson. We also give a saddlepoint approximation for the permutation test. Numerical examples are given to illustrate the accuracy of the saddlepoint approximation and the improvement in the power of the tests compared to the classical statistics in the case of long tailed error distributions and no loss of power for normal error distributions.