A Vectorial Notion of Skewness and Its Use in Testing for Multivariate Symmetry

By modifying the statistic of Malkovich and Afifi (1973), we introduce and study the properties of a notion of multivariate skewness that provides both a magnitude and an overall direction for the skewness present in multivariate data. This notion leads to a test statistic for the nonparametric null hypothesis of multivariate symmetry. Under mild assumptions, we find the asymptotic distribution of the test statistic and evaluate, by simulation, …