Stochastic Orderings of Multivariate Elliptical Distributions

Abstract

Let $\mathbf{X}$ and $\mathbf{X}$ be two $n$-dimensional elliptical random vectors, we establish an identity for $E[f(\mathbf{Y})]-E[f(\mathbf{X})]$, where $f:{\mathbb{R}}^n\to \mathbb{R}$ fulfilling some regularity conditions. Using this identity we provide a unified derivation of sufficient and necessary conditions for classifying multivariate elliptical random vectors according to several main integral stochastic orders. As a consequence we obtain new inequalities by applying it to multivariate elliptical distributions. The results generalize the corresponding ones for multivariate normal random vectors in the literature.

arXiv comment21pages

References in corpus (5)

• Concentration of measure and spectra of random matrices: Applications to correlation matrices, elliptical distributions and beyond
• A Note on Applications of Stochastic Ordering to Control Problems in Insurance and Finance
• The linear stochastic order and directed inference for multivariate ordered distributions
• Comparison inequalities and fastest-mixing Markov chains
• A New Class of Symmetric Distributions Including the Elliptically Symmetric Logistic

Cited by in corpus (1)

• Generalized Location-Scale Mixtures of Elliptical Distributions: Definitions and Stochastic Comparisons