A Useful Property of Best Linear Unbiased Predictors with Applications to Life-Testing

Doganaksoy, Necip; Balakrishnan, N.

doi:10.1080/00031305.1997.10473581

Cited by 18 publications

(7 citation statements)

References 7 publications

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“…This example uses a normally distributed Type-II right censored data, considered earlier by Doganaksoy and Balakrishnan (1997). A life-test with n = 10 resulted in a Type-II censored sample of r = 5 failure times as 87.0, 92.8, 117.1, 133.6 and 138.6.…”

Section: Numerical Illustrationmentioning

confidence: 99%

“…It is important to mention that the above mentioned BLUEs (μ and σ) and BLUP ( Xs:n ) possess several interesting properties. Interested readers may refer to Balakrishnan and Rao (1997), Doganaksoy and Balakrishnan (1997) and Rao (1998, 2003) for details. Recently, Balakrishnan and Bhattacharya (2021) derived explicit expressions for the joint BLUPs of two future order statistics by minimizing the determinant of the variance-covariance matrix of the predictors, and also showed the non-existence of joint BLUPs when three or more order statistics are considered.…”

Section: Introductionmentioning

confidence: 99%

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

Bhattacharya¹

2021

Preprint

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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.

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Section: Numerical Illustrationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Bhattacharya¹

2021

Preprint

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“…Doganskoy and Balakrishnan (1997), Haslett (1999) and quite probably others have drawn attention to this identity in the context of estimating U ≡ β. The proof in Haslett (1999), though simple, relies on maximum likelihood principles for Y ∼ N.Xβ, V /; in Doganskoy and Balakrishnan (1997) the proof is for best linear unbiased prediction but relies on the inverse matrix partitioning identities in Christensen et al (1992). The statement above is more general than both and the proof below is more simple.…”

Section: The Delete = Replace Identitymentioning

confidence: 99%

Application of ‘Delete = Replace’ to Deletion Diagnostics for Variance Component Estimation in the Linear Mixed Model

Haslett

Dillane²

2003

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary. ‘Delete = replace’ is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood estimation for the linear mixed model. We present a new, fast, transparent and approximate computational procedure, arising as a by‐product of the fitting process. We illustrate the effect of the deletion of individual observations, of ‘subjects’ and of arbitrary subsets. Central to the identity and its application is the conditional residual.

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“…extended the idea in the setup of ordered data. Several interested properties of marginal BLUP was discussed by Balakrishnan and Rao (1997), Doganaksoy and Balakrishnan (1997) and Rao (1998, 2003). The prediction problem arise in finding the system failure time of a ncomponent parallel system where the first few component failure times are observed.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous best linear invariant prediction of future order statistics for location-scale and scale families and associated optimality properties

Bhattacharya¹

2021

Preprint

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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 ℓ future order statistics. Both scale and location-scale families of distributions are considered as the parent distribution for the development of results.

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A Useful Property of Best Linear Unbiased Predictors with Applications to Life-Testing

Cited by 18 publications

References 7 publications

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

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

Application of ‘Delete = Replace’ to Deletion Diagnostics for Variance Component Estimation in the Linear Mixed Model

Simultaneous best linear invariant prediction of future order statistics for location-scale and scale families and associated optimality properties

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