On conditional skewness with applications to environmental data

The statistical literature contains many univariate and multivariate skewness measures that allow two datasets to be compared, some of which are defined in terms of quantile values. In most situations, the comparison between two random vectors focuses on univariate comparisons of conditional random variables truncated in quantiles; this kind of comparison is of particular interest in the environmental sciences. In this work, we describe a new approach to comparing skewness in terms of the univariate convex transform ordering proposed by van Zwet (Convex transformations of random variables. Mathematical Centre Tracts, Amsterdam, 1964), associated with skewness as well as concentration. The key to these comparisons is the underlying dependence structure of the random vectors. Below we describe graphical tools and use several examples to illustrate these comparisons.The research of Félix Belzunce, Julio Mulero and José María Ruíz is partially funded by the Ministerio de Economía y Competitividad (Spain) under Grant MTM2012-34023-FEDER. Alfonso Suárez-Llorens acknowledges support received from the Ministerio de Economía y Competitividad (Spain) under Grant MTM2014-57559-P

Canonical transformations of skew-normal variates

Independent component analysis, Normalizing transformations, Principal components analysis, Skewness, Kurtosis, 62F03, 62E17, 62P25,