Prediction via L- statistics in multivariate elliptical distributions

Prediction via L- statistics in multivariate elliptical distributions

In this paper, by considering a (k + t) -dimensional random vector (x", Y?") t Xelf, Yelf having a multivariate elliptical distribution. we derive the exact joint distribution of X and linear combinations of order statistics from Y, as a mixture of multivariate unified skew-elliptical distributions. This mixture representation enables us to predict X based on a linear combination of order statistics from Y, when k c 1 and the kernel distributions are normal and t.