Chapter 3 - Multivariate stochastic orders

Abstract

In this chapter, we introduce and study some of the main multivariate stochastic orders that we can find in the literature. Again, the list is not exhaustive and the idea of this chapter is to give the reader a manageable contact with the topic of stochastic orders in the multivariate case. We provide formal definitions and some results on sufficient conditions for the multivariate stochastic orders to hold, with special emphasis in the case of random vectors with the same copula. We also focus our attention to the derivation of comparisons of convolutions when the addends are possibly dependent. Finally, we provide a section on applications to the comparison of conditionally independent random vectors and ordered data.