Nonparametric inference for stochastic linear hypotheses: Application to high-dimensional data

The Mann--Whitney--Wilcoxon rank sum test is limited to comparison of two groups with univariate responses. In this paper, we introduce a class of stochastic linear hypotheses that addresses these limitations within a nonparametric setting. We formulate hypotheses for simultaneous comparisons of several, multivariate response groups, without modelling the response distributions. Inference is developed based on U-statistics theory and an exchangeability assumption. The latter condition is required to identify testable hypotheses for high-dimensional response vectors, such as those arising in genomic and psychosocial research. The methodology is illustrated with two real-data applications. Copyright Biometrika Trust 2004, Oxford University Press.