Multivariate Order Statistics Induced by Ordering Linear Combinations of Components of Multivariate Elliptical Random Vectors

In this chapter, by considering a np-dimensional random vector X1⊤,…,Xn⊤⊤$$\left ( {\mathbf {X}}_{1}^\top ,\ldots ,{\mathbf {X}}_{n}^\top \right ) ^\top $$, Xi∈ℝp$${\mathbf {X}}_{i} \in \mathbb {R}^{p}$$, i = 1, …, n, having a multivariate elliptical distribution, we derive the exact distribution of multivariate order statistics induced by ordering linear combinations of the components. These induced multivariate order statistics are often …