The Joint Covariance Structure of Ordered Symmetrically Dependent Observations and Their Concomitants of Order Statistics

We considered the ordered components, Y , of a multivariate random variable, Y, with covariance matrix Σ11 and the vector, Z , of concomitantly or induced ordered components of a secondary random vector, Z, with covariance matrix Σ22. Assuming that Σ11, Σ22 and the covariance structure between Y and Z are permutation-symmetric, the joint covariance structure for Y and Z 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.