The joint covariance structure of ordered symmetrically dependent observations and their concomitants of order statistics

We considered the ordered components, , of a multivariate random variable, Y, with covariance matrix [Sigma]11 and the vector, , of concomitantly or induced ordered components of a secondary random vector, Z, with covariance matrix [Sigma]22. Assuming that [Sigma]11, [Sigma]22 and the covariance structure between Y and Z are permutation symmetric, the joint covariance structure for and is obtained. The case in which the joint probability distribution of (Y,Z) is multivariate normal leads to an explicit formulation of the covariances of interest.