• Genomics & Informatics
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• v.12 no.4
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• pp.254-260
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• 2014

Best linear unbiased prediction (BLUP) has been used to estimate the fixed effects and random effects of complex traits. Traditionally, genomic relationship matrix-based (GRM) and random marker-based BLUP analyses are prevalent to estimate the genetic values of complex traits. We used three methods: GRM-based prediction (G-BLUP), random marker-based prediction using an identity matrix (so-called single-nucleotide polymorphism [SNP]-BLUP), and SNP-SNP variance-covariance matrix (so-called SNP-GBLUP). We used 35,675 SNPs and R package "rrBLUP" for the BLUP analysis. The SNP-SNP relationship matrix was calculated using the GRM and Sherman-Morrison-Woodbury lemma. The SNP-GBLUP result was very similar to G-BLUP in the prediction of genetic values. However, there were many discrepancies between SNP-BLUP and the other two BLUPs. SNP-GBLUP has the merit to be able to predict genetic values through SNP effects.

• The Korean Journal of Applied Statistics
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• v.6 no.1
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• pp.95-103
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• 1993

Necessary and sufficient conditions for the equality between the best linear unbiased estimators in two linear models with different covariance matrices, $V_1 and V_2$, say, are derived. Various applications of this discovery are also given. Necessary and sufficient conditions for the equality between the best linear unbiased estimator and the ordinary least squares estimator are discussed related to this topic.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.807-815
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• 2002

We consider a more general linear regression super-population model than the one of Chaudhuri and Stronger(1992) . We can find the same type of the best linear unbiased(BLU) predictor as that of Chaudhuri and Stenger and see that the optimal design is again a purposive one which prescribes choosing one of the samples of size n which has $\chi$ closest to $\bar{X}$.

• Journal of the Korean Statistical Society
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• v.29 no.2
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• pp.231-245
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• 2000

This paper considers a linear regression model with space and time data in where the disturbances follow spatially correlated error components. We provide the best linear unbiased predictor for the one way error components. We provide the best linear unbiased predictor for the one way error component model with spatial autocorrelation. Further, we derive two diagnostic test statistics for the assessment of model specification due to spatial dependence and random effects as an application of the Lagrange Multiplier principle.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.980-983
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• 1996

A new version of the discrete-time optimal FIR (finite impulse response) filter utilizing only the measurements of finite sliding estimation window is suggested for linear time-invariant state-space models. This filter is called the BLUFIR (best linear unbiased finite impulse response) filter since it provides the BLUE (best linear unbiased estimate) of the state obtained from the measurements of the estimation window. It is shown that the BLUFIR filter has the deadbeat property when there are no noises in the estimation window.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.69-79
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• 1996

• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.153-161
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• 2009

We consider a logistic model with random effects as the superpopulation for estimating the small area pro-portions. The best linear unbiased predictor under linear mired model is popular in small area estimation. We use this type of estimator under logistic mixed motel for the small area proportions, on which the estimation of mean squared error is also discussed. Two kinds of estimation methods, the parametric bootstrap and the linear approximation will be compared through a Monte Carlo study in the respects of the normality assumption on the random effects distribution and also the magnitude of sample sizes on the approximation.

• The Mathematical Education
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• v.22 no.2
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• pp.27-29
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• 1984

• International Journal of Reliability and Applications
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• v.8 no.1
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• pp.1-16
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• 2007

In this paper, we derive exact explicit expressions for the triple and quadruple moments of the lower record values from inverse the Weibull (IW) distribution. Next, we present and calculate the coefficients of the best linear unbiased estimates of the location and scale parameters of IW distribution (BLUEs) for different choices of the shape parameter and records size. We then use the higher order moments and the calculated BLUEs to compute the mean, variance, and the coefficients of skewness and kurtosis of certain linear functions of lower record values. By using the coefficients of the skewness and kurtosis, we develop approximate confidence intervals for the location and scale parameters of the IW distribution using Edgeworth approximate values and then compare them with the corresponding intervals constructed through Monte Carlo simulations. Finally, we apply the findings of the paper to some simulated data.

• Asian-Australasian Journal of Animal Sciences
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• v.28 no.11
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• pp.1551-1557
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• 2015

The missing heritability has been a major problem in the analysis of best linear unbiased prediction (BLUP). We introduced the traditional genome-wide association study (GWAS) into the BLUP to improve the heritability estimation. We analyzed eight pork quality traits of the Berkshire breeds using GWAS and BLUP. GWAS detects the putative quantitative trait loci regions given traits. The single nucleotide polymorphisms (SNPs) were obtained using GWAS results with p value <0.01. BLUP analyzed with significant SNPs was much more accurate than that with total genotyped SNPs in terms of narrow-sense heritability. It implies that genomic estimated breeding values (GEBVs) of pork quality traits can be calculated by BLUP via GWAS. The GWAS model was the linear regression using PLINK and BLUP model was the G-BLUP and SNP-GBLUP. The SNP-GBLUP uses SNP-SNP relationship matrix. The BLUP analysis using preprocessing of GWAS can be one of the possible alternatives of solving the missing heritability problem and it can provide alternative BLUP method which can find more accurate GEBVs.