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


  • Jeanne Kowalski


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.

Suggested Citation

  • Jeanne Kowalski, 2004. "Nonparametric inference for stochastic linear hypotheses: Application to high-dimensional data," Biometrika, Biometrika Trust, vol. 91(2), pages 393-408, June.
  • Handle: RePEc:oup:biomet:v:91:y:2004:i:2:p:393-408

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    References listed on IDEAS

    1. Eric Schoen, 1999. "Designing fractional two-level experiments with nested error structures," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 495-508.
    2. GOOS, Peter, "undated". "The usefulness of optimal design for generating blocked and split-plot response surface experiments," Working Papers 2005033, University of Antwerp, Faculty of Applied Economics.
    3. D. R. Bingham & E. D. Schoen & R. R. Sitter, 2004. "Designing fractional factorial split-plot experiments with few whole-plot factors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(2), pages 325-339.
    4. Bradley Jones & Peter Goos, 2007. "A candidate-set-free algorithm for generating "D"-optimal split-plot designs," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(3), pages 347-364.
    5. C. J. Brien & R. A. Bailey, 2006. "Multiple randomizations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 571-609.
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    Cited by:

    1. D. Gunzler & W. Tang & N. Lu & P. Wu & X. Tu, 2014. "A Class of Distribution-Free Models for Longitudinal Mediation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 543-568, October.

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