On simultaneous best linear unbiased prediction of future order statistics and associated properties

TL;DR

This paper develops explicit joint BLUPs for predicting two or more future unobserved order statistics based on observed data, demonstrating their optimality and extending to multiple future statistics.

Contribution

It introduces explicit joint BLUPs for multiple future order statistics and proves their optimality in terms of mean squared error dominance.

Findings

BLUPs are trace-efficient and determinant-efficient.

BLUPs possess complete mean squared predictive error matrix dominance.

Results extend to any number of future order statistics.

Abstract

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.