Distributional results for L-statistics based on random vectors with multivariate elliptical distributions

We consider random vectors X-KX1 and Y-Nxi having a multivariate elliptical joint distribution, and derive the exact joint distribution of X and L-statistics from Y, as a mixture of multivariate unified skew-elliptical distributions. This mixture representation enables us to predict X based on L-statistics from Y, and vice versa, when K = 1 and with normal and t-distributions. Our results extend and generalize previous ones in two ways: first, we consider a general multivariate set-up for which K >= 1 and N >= 2, and second, we adopt the multivariate elliptical distribution to include previous multivariate normal and t-formulations as special cases.