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Robust asymptotic tests for the equality of multivariate coefficients of variation

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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.

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Notes

  1. At distribution F, the weight function was set to \(I_{[0,q_{\delta }]}\) with \(\delta =0.025\) and \(q_{\delta }= G^{-1}(1-\delta )\) where \(G(t)={\mathbb {P}}_{F}[\mathbf {X}^t\mathbf {X}\le t]\).

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Acknowledgments

The authors would like to express their thanks to Professor A. Albert (School of Public Health, University of Liege) for making the EQA data available. This work was partially supported by the IAP Research Network P7/06 of the Belgian State. They also thank the referees for providing constructive comments and helpful suggestions.

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Correspondence to Stephanie Aerts.

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Aerts, S., Haesbroeck, G. Robust asymptotic tests for the equality of multivariate coefficients of variation. TEST 26, 163–187 (2017). https://doi.org/10.1007/s11749-016-0504-4

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