Estimation of the best linear unbiased predictor for the mean with unequal sample sizes

2012 ◽  
Vol 9 (5) ◽  
pp. 515-519
Author(s):  
Poduri S.R.S. Rao
Keyword(s):  
Sample Sizes ◽  
Best Linear Unbiased Predictor ◽  
Best Linear Unbiased ◽  
The Mean ◽  
Unequal Sample Sizes

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.

scholarly journals Genetic analysis of three maize husk traits by QTL mapping in a maize-teosinte population

BMC Genomics ◽  
2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Xiaolei Zhang ◽  
Ming Lu ◽  
Aiai Xia ◽  
Tao Xu ◽  
Zhenhai Cui ◽  
...  
Keyword(s):  
Phenotypic Variation ◽  
Genetic Basis ◽  
Molecular Breeding ◽  
Best Linear Unbiased Predictor ◽  
Maize Line ◽  
Maize Varieties ◽  
Outer Covering ◽  
High Heritability ◽  
Best Linear Unbiased ◽  
Variation Explained

Abstract Background The maize husk consists of numerous leafy layers and plays vital roles in protecting the ear from pathogen infection and dehydration. Teosinte, the wild ancestor of maize, has about three layers of small husk outer covering the ear. Although several quantitative trait loci (QTL) underlying husk morphology variation have been reported, the genetic basis of husk traits between teosinte and maize remains unclear. Results A linkage population including 191 BC2F8 inbred lines generated from the maize line Mo17 and the teosinte line X26–4 was used to identify QTL associated with three husk traits: i.e., husk length (HL), husk width (HW) and the number of husk layers (HN). The best linear unbiased predictor (BLUP) depicted wide phenotypic variation and high heritability of all three traits. The HL exhibited greater correlation with HW than HN. A total of 4 QTLs were identified including 1, 1, 2, which are associated with HL, HW and HN, respectively. The proportion of phenotypic variation explained by these QTLs was 9.6, 8.9 and 8.1% for HL, HN and HW, respectively. Conclusions The QTLs identified in this study will pave a path to explore candidate genes regulating husk growth and development, and benefit the molecular breeding program based on molecular marker-assisted selection to cultivate maize varieties with an ideal husk morphology.

A method for reducing inbreeding with Best Linear Unbiased Prediction

1993 ◽  
Vol 1993 ◽  
pp. 33-33
Author(s):  
B Grundy ◽  
WG Hill
Keyword(s):  
Best Linear Unbiased Prediction ◽  
Breeding Value ◽  
Best Linear Unbiased Predictor ◽  
Linear Unbiased Prediction ◽  
Genetic Merit ◽  
Selection Decisions ◽  
Best Linear Unbiased ◽  
Estimated Breeding Value ◽  
Commercial Environment ◽  
Unbiased Prediction

An optimum way of selecting animals is through a prediction of their genetic merit (estimated breeding value, EBV), which can be achieved using a best linear unbiased predictor (BLUP) (Henderson, 1975). Selection decisions in a commercial environment, however, are rarely made solely on genetic merit but also on additional factors, an important example of which is to limit the accumulation of inbreeding. Comparison of rates of inbreeding under BLUP for a range of hentabilities highlights a trend of increasing inbreeding with decreasing heritability. It is therefore proposed that selection using a heritability which is artificially raised would yield lower rates of inbreeding than would otherwise be the case.

scholarly journals The Probability That a Measurement Falls within a Range of Standard Deviations from an Estimate of the Mean

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Louis M. Houston
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
General Equation ◽  
Sample Sizes ◽  
The Mean ◽  
Standard Deviations ◽  
Intermediate Value ◽  
Theoretical Results

We derive a general equation for the probability that a measurement falls within a range of n standard deviations from an estimate of the mean. So, we provide a format that is compatible with a confidence interval centered about the mean that is naturally independent of the sample size. The equation is derived by interpolating theoretical results for extreme sample sizes. The intermediate value of the equation is confirmed with a computational test.

scholarly journals Estimating Parametersof Gumbel Distribution For Maximum Values By using Simulation

2016 ◽  
Vol 13 (4) ◽  
pp. 707-713
Author(s):  
Baghdad Science Journal
Keyword(s):  
Gumbel Distribution ◽  
Estimation Methods ◽  
Sample Sizes ◽  
Random Data ◽  
The Real ◽  
The Mean ◽  
Distribution Type

In this research estimated the parameters of Gumbel distribution Type 1 for Maximum values through the use of two estimation methods:- Moments (MoM) and Modification Moments(MM) Method. the Simulation used for comparison between each of the estimation methods to reach the best method to estimate the parameters where the simulation was to generate random data follow Gumbel distributiondepending on three models of the real values of the parameters for different sample sizes with samples of replicate (R=500).The results of the assessment were put in tables prepared for the purpose of comparison, which made depending on the mean squares error (MSE).

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