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Multivariate nonparametric tests in a randomized complete block design

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  • Möttönen, J.
  • Hüsler, J.
  • Oja, H.

Abstract

In this paper multivariate extensions of the Friedman and Page tests for the comparison of several treatments are introduced. Related unadjusted and adjusted treatment effect estimates for the multivariate response variable are also found and their properties discussed. The test statistics and estimates are analogous to the traditional univariate methods. In test constructions, the univariate ranks are replaced by multivariate spatial ranks (J. Nonparam. Statist. 5 (1995) 201). Asymptotic theory is developed to provide approximations for the limiting distributions of the test statistics and estimates. Limiting efficiencies of the tests and treatment effect estimates are found in the multivariate normal and t distribution cases. The tests are rotation invariant only, but affine invariant versions can be easily constructed. The theory is illustrated by an example.

Suggested Citation

  • Möttönen, J. & Hüsler, J. & Oja, H., 2003. "Multivariate nonparametric tests in a randomized complete block design," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 106-129, April.
    • Handle: RePEc:eee:jmvana:v:85:y:2003:i:1:p:106-129
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    References listed on IDEAS

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    1. Hannu Oja, 1999. "Affine Invariant Multivariate Sign and Rank Tests and Corresponding Estimates: a Review," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 319-343, September.
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    Cited by:

    1. Hannu Oja & Davy Paindaveine & Sara Taskinen, 2009. "Parametric and nonparametric test for multivariate independence in IC models," Working Papers ECARES 2009_018, ULB -- Universite Libre de Bruxelles.
    2. Li, Chen, 2020. "Designing a short-term load forecasting model in the urban smart grid system," Applied Energy, Elsevier, vol. 266(C).
    3. Paindaveine, Davy, 2009. "On Multivariate Runs Tests for Randomness," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1525-1538.
    4. Nevalainen, Jaakko & Möttönen, Jyrki & Oja, Hannu, 2008. "A spatial rank test and corresponding estimators for several samples," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 661-668, April.
    5. Seija Sirkiä & Sara Taskinen & Hannu Oja & David Tyler, 2009. "Tests and estimates of shape based on spatial signs and ranks," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(2), pages 155-176.

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