ABSTRACT Existing high-dimensional inferential methods for comparing multiple groups test hypotheses are formulated in terms of mean vectors or location parameters. These methods are applicable mainly for metric data. Furthermore, the mean-based methods assume that moments exist and the nonparametric (location-based) ones assume elliptical-contoured distributions for the populations. In this paper, a fully nonparametric (rank-based) method is proposed. The method is applicable for metric as well as non-metric data and, hence, is applicable for ordered categorical as well as skewed and heavy tailed data. To develop the theory, we prove a novel result for studying asymptotic behaviour of quadratic forms in ranks. Simulation study shows that the developed rank-based method performs comparably well with mean-based methods when the assumptions of those methods are satisfied. However, it has significantly superior power for heavy tailed distributions with the possibility of outliers. The rank method is applied to an EEG data with the objective of examining associations between alcohol use and change in brain function.

中文翻译：

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高维基于秩的推理

摘要 现有的用于比较多组测试假设的高维推理方法是根据平均向量或位置参数制定的。这些方法主要适用于度量数据。此外，基于均值的方法假设存在矩，而非参数（基于位置的）方法假设总体呈椭圆轮廓分布。在本文中，提出了一种完全非参数（基于秩）的方法。该方法适用于度量数据和非度量数据，因此适用于有序分类数据以及偏斜和重尾数据。为了发展该理论，我们证明了研究秩中二次形式的渐近行为的新结果。模拟研究表明，当满足这些方法的假设时，所开发的基于秩的方法与基于均值的方法性能相当。然而，它对于可能存在异常值的重尾分布具有显着优越的能力。等级方法应用于 EEG 数据，目的是检查饮酒与大脑功能变化之间的关联。