Some stochastic orderings of multivariate skew-normal random vectors

In this paper, we investigate some multivariate integral stochastic orderings of skew-normal random vectors. We derive the results of the sufficient and/or necessary conditions by applying an identity for $Ef(\mathbf{Y})-Ef(\mathbf{X})$, where $\mathbf{X}$ and $\mathbf{Y}$ are multivariate skew-normal random vectors, $f$ satisfies some weak regularity condition. The integral orders considered here are the componentwise convex, copositive, completely-positive orderings and their corresponding increasing ones as well as linear forms of stochastic orderings, which play a vital role in transforming the unmanageable multivariate components into an easy-to-handle univariate variable.