Permutation tests enable testing statistical hypotheses in situations when the distribution of the test statistic is complicated or not available. In some situations, the test statistic under investigation is multivariate, with the multiple testing problem being an important example. The corresponding multivariate permutation tests are then typically based on a suitableone-dimensional transformation of the vector of partial permutation p-values via so called combining functions. This paper proposes a new approach that utilizes the optimal measure transportation concept. The final single p-value is computed from the empirical center-outward distribution function of the permuted multivariate test statistics. This method avoids computation of the partial p-values and it is easy to be implemented. In addition, it allows to compute and interpret contributions of the components of the multivariate test statistic to the non-conformity score and to the rejection of the null hypothesis. Apart from this method, the measure transportation is applied also to the vector of partial p-values as an alternative to the classical combining functions. Both techniques are compared with the standard approaches using various practical examples in a Monte Carlo study. An application on a functional data set is provided as well.

翻译：置换检验能够在检验统计量分布复杂或未知的情况下进行统计假设检验。在某些情形下，被研究的检验统计量具有多变量性质，多重检验问题即是一个重要实例。相应的多变量置换检验通常通过所谓的组合函数，对部分置换p值向量进行合适的单维变换。本文提出一种利用最优测度传输概念的新方法。最终单一p值通过置换后多变量检验统计量的经验中心外扩分布函数计算得出。该方法避免了计算部分p值，且易于实现。此外，该方法能够计算并解释多变量检验统计量各分量对非一致性分数及原假设拒绝的贡献。除本方法外，测度传输还被应用于部分p值向量，作为经典组合函数的替代方案。通过蒙特卡洛研究中的各种实际案例，将这两种技术与标准方法进行对比分析。此外，还提供了在函数型数据集上的应用实例。