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Abstract :
[en] In the univariate context, coefficients of variation (CVs) are widely used to compare the relative dispersion of a variable across several populations. When the comparison is based on p characteristics, however, side-by-side comparison of marginal CVs may lead to contradictory results.
In response, several proposals for multivariate coefficients of variation (MCVs) have been introduced and used in the literature. These are measures of relative dispersion that summarize the multivariate information into one single index. Depending on the context (flat data, invariance requirement,...), one of these proposals might be more appropriate. Whichever definition is chosen however, in practice, all coefficients can be estimated by plugging any pair of location and covariance estimators in their defintion.
In this talk, some of the properties (bias, robustness,...) of the resulting estimators will be reviewed and discussed. The construction of confidence intervals and tests for comparing the relative dispersion in multivariate data will also be considered.
Examples related to finance or analytical chemistry will be used throughout the talk as illustration.
