On some multivariate descriptive statistics based on multivariate signs and ranks

In this research, several notions of multivariate symmetry and multivariate medians are discussed. We consider a generalization of univariate quantiles to the multivariate context and producing quantile contour plots. Also some descriptive nonparametric multivariate measures like scale curves, skewness and kurtosis are considered. We plot volume functional as a scale curve which produces two dimensional characterization of the spread of a multivariate distribution of any dimension. We also note bivariate generalization of the boxplot. Since lp-ranks are not affine equivariant, thus scale curves and boxplots based on lp-ranks are not affine equivariant too. Consequently, transformation retransformation procedure is used to construct affine equivariant multivariate lp-quantiles and lp-ranks. Since the real data are not always symmetric we consider multivariate g-and-h distribution which is a skew symmetric distribution. All the descriptive measures are discussed using simulated data from bivariate normal, bivariate Laplace and t-distribution with 4 degrees of freedom and on some real data sets as well.

Author dc:creator

• NELUKA DEVPURA

• lp-Signs; lp-Ranks; lp-Quantiles; Affine Equivariance; Multivariate Medians