Nonparametric methods for unbalanced multivariate data and many factor levels

Solomon W. Harrar, Arne C. Bathke

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


We propose different nonparametric tests for multivariate data and derive their asymptotic distribution for unbalanced designs in which the number of factor levels tends to infinity (large a, small ni case). Quasi gratis, some new parametric multivariate tests suitable for the large a asymptotic case are also obtained. Finite sample performances are investigated and compared in a simulation study. The nonparametric tests are based on separate rankings for the different variables. In the presence of outliers, the proposed nonparametric methods have better power than their parametric counterparts. Application of the new tests is demonstrated using data from plant pathology.

Original languageEnglish
Pages (from-to)1635-1664
Number of pages30
JournalJournal of Multivariate Analysis
Issue number8
StatePublished - Sep 2008


  • 62G10
  • 62G20
  • 62H10
  • 62H15
  • 62J10
  • Multivariate analysis of variance
  • Nonnormality
  • Nonparametric model
  • Ordinal data
  • Rank statistic
  • Unbalanced design

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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