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

Narayanaswamy Balakrishnan and Ritwik Bhattacharya

Journal of Multivariate Analysis, 2022, vol. 188, issue C

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. Both scale and location-scale family of distributions are considered as the parent distribution for the underlying random variables.

Keywords: Best linear unbiased predictor; Best linear unbiased estimator; Complete mean squared predictive error matrix dominance; Determinant-efficient predictor; Mean squared predictive error; Order statistics; Trace-efficient predictor (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.jmva.2021.104854

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