<scp>EBLUPs</scp>: Empirical Best Linear Unbiased Predictors

Haslett, Stephen; Welsh, A. H.

doi:10.1002/9781118445112.stat08180

Cited by 5 publications

(3 citation statements)

References 20 publications

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“…In Stage 1, the cultivar means were estimated via empirical best linear unbiased estimation (EBLUE). The term “empirical” here refers to the fact that the variance components must be estimated from the data (Forkman, 2013; Harville, 1991; Haslett & Welsh, 2019). In Stage 2, there were two options, unweighted and weighted.…”

Section: Methodsmentioning

confidence: 99%

Cross‐validation of stagewise mixed‐model analysis of Swedish variety trials with winter wheat and spring barley

et al. 2020

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In cultivar testing, linear mixed models have been used routinely to analyze multienvironment trials. A single‐stage analysis is considered as the gold standard, whereas two‐stage analysis produces similar results when a fully efficient weighting method is used, namely when the full variance–covariance matrix of the estimated means from Stage 1 is forwarded to Stage 2. However, in practice, this may be hard to do and a diagonal approximation is often used. We conducted a cross‐validation with data from Swedish cultivar trials on winter wheat (Triticum aestivum L.) and spring barley (Hordeum vulgare L.) to assess the performance of single‐stage and two‐stage analyses. The fully efficient method and two diagonal approximation methods were used for weighting in the two‐stage analyses. In Sweden, cultivar recommendation is delineated by zones (regions), not individual locations. We demonstrate the use of best linear unbiased prediction (BLUP) for cultivar effects per zone, which exploits correlations between zones and thus allows information to be borrowed across zones. Complex variance–covariance structures were applied to allow for heterogeneity of cultivar × zone variance. The single‐stage analysis and the three weighted two‐stage analyses all performed similarly. Loss of information caused by a diagonal approximation of the variance–covariance matrix of adjusted means from Stage 1 was negligible. As expected, BLUP outperformed best linear unbiased estimation. Complex variance–covariance structures were dispensable. To our knowledge, this study is the first to use cross‐validation for comparing single‐stage analyses with stagewise analyses.

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Section: Methodsmentioning

confidence: 99%

Cross‐validation of stagewise mixed‐model analysis of Swedish variety trials with winter wheat and spring barley

et al. 2020

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“…As detailed in Haslett [14] Das and Haslett [10] for unit-level models, much depends on the type of data available. In their original forms, both EBP and ELL are mixed linear models from which best linear unbiased predictions (BLUPs) (Haslett and Puntanen [15] ) or more strictly empirical best linear unbiased predictions (EBLUPs) (Haslett and Welsh [16] ) are generally derived and used to create SAEs. As an aside, EBP uses EBLUP conditional on the sample for the SAEs for the sampled small areas, but can only use empirical best linear unbiased estimation (based on the fixed effects only) for unsampled areas, which is why the accuracy for sampled areas is generally better.…”

Section: Sae Models and Modellingmentioning

confidence: 99%

Discussion

Haslett

2024

Calcutta Statistical Association Bulletin

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“…by ignoring the cross-product term, noting that there is no-closed form expression for the MSPE( ˆ PEB i ) (Haslett & Welsh 2019). We will report the magnitude of ignored M 3i in the simulation study section.…”

Section: Pseudo-empirical Best Predictormentioning

confidence: 99%

Small area estimation under a semi‐parametric covariate measured with error

Sefidkar

Torabi²,

Kavousi³

2022

Aus NZ J of Statistics

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In recent years, small area estimation has played an important role in statistics as it deals with the problem of obtaining reliable estimates for parameters of interest in areas with small or even zero sample sizes corresponding to population sizes. Nested error linear regression models are often used in small area estimation assuming that the covariates are measured without error and also the relationship between covariates and response variable is linear. Small area models have also been extended to the case in which a linear relationship may not hold, using penalised spline (P-spline) regression, but assuming that the covariates are measured without error. Recently, a nested error regression model using a P-spline regression model, for the fixed part of the model, has been studied assuming the presence of measurement error in covariate, in the Bayesian framework. In this paper, we propose a frequentist approach to study a semi-parametric nested error regression model using P-splines with a covariate measured with error. In particular, the pseudo-empirical best predictors of small area means and their corresponding mean squared prediction error estimates are studied. Performance of the proposed approach is evaluated through a simulation and also by a real data application.

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EBLUPs: Empirical Best Linear Unbiased Predictors

Cited by 5 publications

References 20 publications

Cross‐validation of stagewise mixed‐model analysis of Swedish variety trials with winter wheat and spring barley

Cross‐validation of stagewise mixed‐model analysis of Swedish variety trials with winter wheat and spring barley

Discussion

Small area estimation under a semi‐parametric covariate measured with error

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