  In this article, the joint best linear unbiased predictors (BLUPs) of two
future unobserved order statistics, based on a set of observed order
statistics, are developed explicitly. It is shown that these predictors are
trace-efficient as well as determinant-efficient BLUPs. More generally, the
BLUPs are shown to possess complete mean squared predictive error matrix
dominance in the class of all linear unbiased predictors of two future
unobserved order statistics. Finally, these results are extended to the case of
simultaneous BLUPs of any $l$ future order statistics.
