Multivariate coefficients of variation: a full inference toolbox

The univariate coefficient of variation (CV) is a widely used measure to compare the relative dispersion of a variable in several populations. When the comparison is based on $p$ characteristics however, side-by-side comparison of marginal CV's may lead to contradictions. Several multivariate coefficients of variation (MCV) have been introduced and used in the literature but, so far, their properties have not been much studied. Based on one of them, i.e. the inverse of the Mahalanobis distance between the mean and the origin, this talk intends to demonstrate the usefulness of MCV's in several domains (finance and analytical chemistry) as well as provide a complete inference toolbox for practitioners. Some exact and approximate confidence intervals are constructed, whose performance is analyzed through simulations. Several bias-correction methods, either parametric or not, are suggested and compared. Finally, since MCV's are used for comparison purposes, some test statistics are proposed for the homogeneity of MCV's in $K$ populations. Throughout the talk, the robustness of the techniques will be discussed. As a by-product, a test statistic allowing to reliably compare $K$ univariate CV's even in presence of outliers will be outlined.