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

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  • Jeanne Kowalski

Abstract

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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    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.
    2. N. Lu & T. Chen & P. Wu & D. Gunzler & H. Zhang & H. He & X.M. Tu, 2014. "Functional response models for intraclass correlation coefficients," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2539-2556, November.
    3. R. Chen & T. Chen & N. Lu & H. Zhang & P. Wu & C. Feng & X.M. Tu, 2014. "Extending the Mann-Whitney-Wilcoxon rank sum test to longitudinal regression analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(12), pages 2658-2675, December.

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