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

Jeanne Kowalski, Jonathan Powell

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)393-408
Number of pages16
Issue number2
StatePublished - 2004


  • Asymptotic distribution
  • Exchangeability assumption
  • U-statistic

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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