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A nonparametric version of Wilks' lambda--Asymptotic results and small sample approximations


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


We propose a nonparametric version of Wilks' lambda (the multivariate likelihood ratio test) and investigate its asymptotic properties under the two different scenarios of either large sample size or large number of samples. For unbalanced samples, a weighted and an unweighted variant are introduced. The unweighted variant of the proposed test appears to be novel also in the normal-theory context. The theoretical results are supplemented by a simulation study with parameter settings that are motivated by clinical and agricultural data, considering in particular the performance for small sample sizes, small number of samples, and varying dimensions. Inference methods based on the asymptotic sampling distribution and a small sample approximation are compared to permutation tests and to other parametric and nonparametric procedures. Application of the proposed method is illustrated by examples.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:10:p:1502-1506

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    References listed on IDEAS

    1. 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.
    2. Gupta, Arjun K. & Harrar, Solomon W. & Fujikoshi, Yasunori, 2006. "Asymptotics for testing hypothesis in some multivariate variance components model under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 148-178, January.
    3. Thompson, G. L., 1990. "Asymptotic distribution of rank statistics under dependencies with multivariate application," Journal of Multivariate Analysis, Elsevier, vol. 33(2), pages 183-211, May.
    4. 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.
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    Cited by:

    1. 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.


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