In this article, we first derive an explicit expression for the marginal best linear invariant predictor (BLIP) of an unobserved future order statistic based on a set of early observed ordered statistics. We then derive the joint BLIPs of two future order statistics and prove that the joint predictors are trace-efficient as well as determinant-efficient linear invariant predictors. More generally, the BLIPs are shown to possess complete mean squared predictive error matrix dominance property in the class of all linear invariant predictors of two future unobserved order statistics. Finally, these results are extended to the case of simultaneous BLIPs of any $\ell$ future order statistics. Both scale and location-scale families of distributions are considered as the parent distribution for the development of results.

翻译：在本文中,我们首先根据一套早期观察的定单统计数据,明确表达未观测的未来顺序统计的边缘最佳线性变差预测仪(BLIP),然后得出两个未来定单统计数据的联合线性预测仪,并证明联合预测仪既具有追踪效率,又具有决定性效率的线性变差预测仪。更一般地说,显示BLIP在两种未来未观测的定单统计数据的所有线性变差预测仪类别中拥有完全平均的正方形预测错误矩阵占支配地位。最后,这些结果扩大到同时出现任何$\ell$的未来定单统计数据的同时线性预测仪。