The 𝑟-𝑑 class predictions in linear mixed models

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Özge Kuran
Keyword(s):  
Mixed Models ◽  
Linear Mixed Models ◽  
Mean Square ◽  
Best Linear Unbiased Predictor ◽  
Principal Components Regression ◽  
Error Matrix ◽  
Numerical Examples ◽  
Best Linear Unbiased ◽  
The Mean ◽  
Mean Square Error Matrix

AbstractIn this paper, we propose the r-d class predictors which are general predictors of the best linear unbiased predictor (BLUP), the principal components regression (PCR) and the Liu predictors in the linear mixed models. Superiorities of the linear combination of the new predictors to each of these predictors are done in the sense of the mean square error matrix criterion. Finally, numerical examples and a simulation study are done to illustrate the findings.

Use of Prediction Methods to Assess Laboratory Bias and Mean Values Associated with an Interlaboratory Study for Method Validation and/or Proficiency Testing

2014 ◽  
Vol 97 (2) ◽  
pp. 624-629 ◽  
Author(s):  
Foster D McClure ◽  
Jung K Lee
Keyword(s):  
Random Variables ◽  
Least Square ◽  
Best Linear Unbiased Predictor ◽  
Least Square Estimator ◽  
Mean Values ◽  
Interlaboratory Studies ◽  
Repeatability And Reproducibility ◽  
Best Linear Unbiased ◽  
The Mean ◽  
The Individual

Abstract Two methods of prediction of random variables, best predictor (BP) and best linear unbiased predictor (BLUP), are discussed as potential statistical methods to predict laboratory true mean and bias values using the sample laboratory mean (yi) from interlaboratory studies. The predictions developed here require that the interlaboratory and/or proficiency study be designed and conducted in a manner consistent with the assumptions of a one-way completely randomized model (CRM). Under the CRM the individual laboratory true mean and bias are not parameters but are defined to be random variables that are unobservable and considered as realized values that cannot be estimated but can be predicted using methods of “prediction.” The BP method is applicable when all salient parameters are known, e.g., the consensus true overall mean (μ) and repeatability and reproducibility components (σr2 and σR2), while the BLUP method is useful when σ2r and σR2 are known, but μ is estimated by the generalized least square estimator. Although the derivations of predictors are obtained by minimizing the mean-square error under the CRM assumptions, the predictors are the expected laboratory true mean and bias given the sample laboratory mean, i.e., conditional expectation.

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