The University of Montana
Department of Mathematical Sciences

Technical report #12/2007

Nonparametric Methods for Unbalanced Multivariate Data

Solomon W. Harrar * and Arne C. Bathke **
*Solomon W. Harrar is Assistant Professor, Department of Mathematical Sciences, University of Montana, 32 Campus Drive, Missoula, MT 59812, USA; Email:
**Arne C. Bathke is Assistant Professor, Department of Statistics, University of Kentucky, 875 Patterson Office Tower, Lexington, KY 40506-0027, USA; Email:


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 nicase). 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.

AMS Subject Classificatios: 62G10, 62G20, 62H10, 62H15, 62J10.

Keywords:Multivariate Analysis of Variance, Nonnormality, Nonparametric Model, Ordinal Data, Rank statistic, Unbalanced Design.

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