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Robust asymptotic tests for the equality of multivariate coefficients of variation

Author

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  • Stephanie Aerts

    (HEC-ULg, University of Liege (ULg, N1))

  • Gentiane Haesbroeck

    (University of Liege (ULg, Polytech 1))

Abstract

In order to easily compare several populations on the basis of more than one feature, multivariate coefficients of variation (MCV) may be used as they allow to summarize relative dispersion in a single index. However, up to date, no test of equality of one or more MCVs has been developed in the literature. In this paper, several classical and robust Wald-type tests are proposed and studied. The asymptotic distributions of the test statistics are derived under elliptical symmetry, and the asymptotic efficiency of the robust versions is compared to the classical tests. Robustness of the proposed procedures is examined through partial and joint influence functions of the test statistic, as well as by means of power and level influence functions. A simulation study compares the performance of the classical and robust tests under uncontaminated and contaminated schemes, and the difference with the usual covariance homogeneity test is highlighted. As a by-product, these tests may also be considered in the univariate context where they yield procedures that are both robust and easy-to-use. They provide an interesting alternative to the numerous parametric tests existing in the literature, which are, in most cases, unreliable in presence of outliers. The methods are illustrated on a real data set.

Suggested Citation

  • Stephanie Aerts & Gentiane Haesbroeck, 2017. "Robust asymptotic tests for the equality of multivariate coefficients of variation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 163-187, March.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:1:d:10.1007_s11749-016-0504-4
    DOI: 10.1007/s11749-016-0504-4
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    References listed on IDEAS

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    Cited by:

    1. Ditzhaus, Marc & Smaga, Łukasz, 2022. "Permutation test for the multivariate coefficient of variation in factorial designs," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    2. Ayanendranath Basu & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2018. "Robust Wald-type tests for non-homogeneous observations based on the minimum density power divergence estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 493-522, July.
    3. Kokonendji, Célestin C. & Puig, Pedro, 2018. "Fisher dispersion index for multivariate count distributions: A review and a new proposal," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 180-193.
    4. Célestin C. Kokonendji & Aboubacar Y. Touré & Amadou Sawadogo, 2020. "Relative variation indexes for multivariate continuous distributions on $$[0,\infty )^k$$[0,∞)k and extensions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 285-307, June.

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