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 sum-
marize 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 statis-
tic, 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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• Robust asymptotic tests for the equality of multivariate coefficients of variation