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Nonparametric methods for unbalanced multivariate data and many factor levels

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  • Harrar, Solomon W.
  • Bathke, Arne C.

Abstract

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.

Suggested Citation

  • Harrar, Solomon W. & Bathke, Arne C., 2008. "Nonparametric methods for unbalanced multivariate data and many factor levels," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1635-1664, September.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:8:p:1635-1664
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    1. Akritas M.G. & Papadatos N., 2004. "Heteroscedastic One-Way ANOVA and Lack-of-Fit Tests," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 368-382, January.
    2. 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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    4. Brunner, Edgar & Munzel, Ulrich & Puri, Madan L., 1999. "Rank-Score Tests in Factorial Designs with Repeated Measures," Journal of Multivariate Analysis, Elsevier, vol. 70(2), pages 286-317, August.
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    Cited by:

    1. Rauf Ahmad, M. & Werner, C. & Brunner, E., 2008. "Analysis of high-dimensional repeated measures designs: The one sample case," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 416-427, December.
    2. Gunawardana, Asanka & Konietschke, Frank, 2019. "Nonparametric multiple contrast tests for general multivariate factorial designs," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 165-180.
    3. Bathke, Arne C. & Harrar, Solomon W. & Madden, Laurence V., 2008. "How to compare small multivariate samples using nonparametric tests," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4951-4965, July.
    4. Giuseppe Pernagallo & Benedetto Torrisi, 2023. "Human capital mobility patterns in the European Union and the financial crisis," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(2), pages 1791-1820, April.
    5. Liu, Chunxu & Bathke, Arne C. & Harrar, Solomon W., 2011. "A nonparametric version of Wilks' lambda--Asymptotic results and small sample approximations," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1502-1506, October.
    6. Bathke, Arne C. & Harrar, Solomon W. & Wang, Haiyan & Zhang, Ke & Piepho, Hans-Peter, 2010. "Series of randomized complete block experiments with non-normal data," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1840-1857, July.
    7. Konietschke, Frank & Bathke, Arne C. & Harrar, Solomon W. & Pauly, Markus, 2015. "Parametric and nonparametric bootstrap methods for general MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 291-301.
    8. Solomon Harrar & Arne Bathke, 2012. "A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 135-165, February.
    9. Dennis Dobler & Sarah Friedrich & Markus Pauly, 2020. "Nonparametric MANOVA in meaningful effects," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 997-1022, August.
    10. Harrar, Solomon W. & Kong, Xiaoli, 2022. "Recent developments in high-dimensional inference for multivariate data: Parametric, semiparametric and nonparametric approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    11. Wang, Haiyan & Akritas, Michael G., 2010. "Rank test for heteroscedastic functional data," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1791-1805, September.
    12. Hasler Mario, 2014. "Multiple Contrast Tests for Multiple Endpoints in the Presence of Heteroscedasticity," The International Journal of Biostatistics, De Gruyter, vol. 10(1), pages 1-12, May.

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