Title: Projection pursuit under skew-normal vectors: An approach oriented to skewness stochastic comparisons
Authors: Jorge Martin Arevalillo - UNED (Spain) [presenting]
Hilario Navarro-Veguillas - UNED / Facultad de Ciencias (Spain)
Abstract: The skewness based projection pursuit problem for vectors that follow a multivariate skew-normal (SN) distribution is revisited. The issue, which is a standard in multivariate data analysis, has a close connection with the canonical transformation of SN vectors. We elaborate on the implications of such a connection in order to define a skewness ordering that allows stochastic comparisons within the family of multivariate SN distributions. The proposed ordering relies on the convex transform ordering between the only skewed component derived from the canonical representation of SN vectors under comparison. Its relationship with standard multivariate skewness measures is also examined and some highlights showing its usefulness in the statistical practice are provided as well.