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D-optimal joint best linear unbiased prediction of order statistics

Joint BLUP

Abstract

In life-testing experiments, it is often of interest to predict unobserved future failure times based on observed early failure times. A point best linear unbiased predictor (BLUP) has been developed in this context by Kaminsky and Nelson (J Am Stat Assoc 70:145–150, 1975). In this article, we develop joint BLUPs of two future failure times based on early failure times by minimizing the determinant of the variance–covariance matrix of the predictors. The advantage of applying joint prediction is demonstrated by using two real data sets. The non-existence of joint BLUPs in certain setups is also discussed.

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Acknowledgements

The authors express their sincere thanks to the anonymous reviewers and the Editor for their valuable comments and suggestions on an earlier version of this manuscript which led to this improved version.

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Correspondence to Ritwik Bhattacharya.

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Balakrishnan, N., Bhattacharya, R. D-optimal joint best linear unbiased prediction of order statistics. Metrika 85, 253–267 (2022). https://doi.org/10.1007/s00184-021-00835-0

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  • DOI: https://doi.org/10.1007/s00184-021-00835-0

Keywords

  • Best linear unbiased estimate (BLUE)
  • Best linear unbiased predictor (BLUP)
  • Location-scale family of distribution
  • Lagrangian method
  • Order statistics
  • Scale family of distributions
  • Type-II right censored samples
  • Variance–covariance matrix