• 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.

• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.187-201
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• 2006

In this paper, we derive recurrence relations for the single and product moments of progressively Type-II right censored order statistics from half logistic distribution. Next, we derive the maximum likelihood estimators (MLEs) of the location and scale parameters of the half logistic distribution. In addition, we use the setup proposed by Balakrishnan and Aggarwala (2000) to compute the approximate best linear unbiased estimates (ABLUEs) of the location and scale parameters. Finally, we point out a simulation study to compare between the efficiency of the techniques considered for the estimation.

• Asian-Australasian Journal of Animal Sciences
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• v.30 no.2
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• pp.149-153
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• 2017

Objective: This study was to determine the relationship between estimated breeding value and phenotype information after farrowing when juvenile selection was made in candidate pigs without phenotype information. Methods: After collecting phenotypic and genomic information for the total number of piglets born by Landrace pigs, selection accuracy between genomic breeding value estimates using genomic information and breeding value estimates of best linear unbiased prediction (BLUP) using conventional pedigree information were compared. Results: Genetic standard deviation (${\sigma}_a$) for the total number of piglets born was 0.91. Since the total number of piglets born for candidate pigs was unknown, the accuracy of the breeding value estimated from pedigree information was 0.080. When genomic information was used, the accuracy of the breeding value was 0.216. Assuming that the replacement rate of sows per year is 100% and generation interval is 1 year, genetic gain per year is 0.346 head when genomic information is used. It is 0.128 when BLUP is used. Conclusion: Genetic gain estimated from single step best linear unbiased prediction (ssBLUP) method is by 2.7 times higher than that the one estimated from BLUP method, i.e., 270% more improvement in efficiency.

• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.1179-1189
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• 2007

In this paper, we estimate the proportion of individuals having health insurance in a given year for several small domains cross-classified by age, sex and other demographic characteristics using the data provided by the National Center for Health Statistics(NCHS). We employ Bayesian as well as frequentist methodology to obtain small domain estimates and the associated measures of precision. One of the new features of our study is that we utilize the survey weights along with the model to derive the small domain estimates.

• Journal of the Korea Society for Simulation
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• v.2 no.1
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• pp.125-133
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• 1993

A statistical method is described for estimation of the unknown constants in a theory using both of the computer simulation data and the real experimental data, The best linear unbiased predictor based on a spatial linear model is fitted from the computer simulation data alone. Then nonlinear least squares estimation method is applied to the real experimental data using the fitted prediction model as if it were the true simulation model. An application to the computational nuclear fusion devices is presented, where the nonlinear least squares estimates of four transport coefficients of the theoretical nuclear fusion model are obtained.

• Journal of the Korean Statistical Society
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• v.4 no.1
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• pp.39-56
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• 1975

Ever since Gauss discussed the least-squares method in 1812 and Bertrand translated Gauss's work in French, the least-squares method has been used for various economic analysis. The justification of the least-squares method was given by Markov in 1912 in connection with the previous discussion by Gauss and Bertrand. The main argument concerned the problem of obtaining the best linear unbiased estimates. In some modern language, the argument can be explained as follow.

• Animal Bioscience
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• v.36 no.7
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• pp.1003-1009
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• 2023

Objective: The objective was to compare (pedigree-based) best linear unbiased prediction (BLUP), genomic BLUP (GBLUP), and single-step GBLUP (ssGBLUP) methods for genomic evaluation of growth traits in a Mexican Braunvieh cattle population. Methods: Birth (BW), weaning (WW), and yearling weight (YW) data of a Mexican Braunvieh cattle population were analyzed with BLUP, GBLUP, and ssGBLUP methods. These methods are differentiated by the additive genetic relationship matrix included in the model and the animals under evaluation. The predictive ability of the model was evaluated using random partitions of the data in training and testing sets, consistently predicting about 20% of genotyped animals on all occasions. For each partition, the Pearson correlation coefficient between adjusted phenotypes for fixed effects and non-genetic random effects and the estimated breeding values (EBV) were computed. Results: The random contemporary group (CG) effect explained about 50%, 45%, and 35% of the phenotypic variance in BW, WW, and YW, respectively. For the three methods, the CG effect explained the highest proportion of the phenotypic variances (except for YW-GBLUP). The heritability estimate obtained with GBLUP was the lowest for BW, while the highest heritability was obtained with BLUP. For WW, the highest heritability estimate was obtained with BLUP, the estimates obtained with GBLUP and ssGBLUP were similar. For YW, the heritability estimates obtained with GBLUP and BLUP were similar, and the lowest heritability was obtained with ssGBLUP. Pearson correlation coefficients between adjusted phenotypes for non-genetic effects and EBVs were the highest for BLUP, followed by ssBLUP and GBLUP. Conclusion: The successful implementation of genetic evaluations that include genotyped and non-genotyped animals in our study indicate a promising method for use in genetic improvement programs of Braunvieh cattle. Our findings showed that simultaneous evaluation of genotyped and non-genotyped animals improved prediction accuracy for growth traits even with a limited number of genotyped animals.

• Asian-Australasian Journal of Animal Sciences
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• v.33 no.10
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• pp.1544-1557
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• 2020

Objective: Genomic selection (GS) is becoming popular in animals' genetic development. We, therefore, investigated the single-step genomic best linear unbiased prediction (ssGBLUP) as tool for GS, and compared its efficacy with the traditional pedigree BLUP (pedBLUP) method. Methods: A total of 9,952 males born between 1997 and 2018 under Hanwoo proven-bull selection program was studied. We analyzed body weight at 12 months and carcass weight (kg), backfat thickness, eye muscle area, and marbling score traits. About 7,387 bulls were genotyped using Illumina 50K BeadChip Arrays. Multiple-trait animal model analyses were performed using BLUPF90 software programs. Breeding value accuracy was calculated using two methods: i) Pearson's correlation of genomic estimated breeding value (GEBV) with EBV of all animals (r_M1) and ii) correlation using inverse of coefficient matrix from the mixed-model equations (r_M2). Then, we compared these accuracies by overall population, info-type (PHEN, phenotyped-only; GEN, genotyped-only; and PH+GEN, phenotyped and genotyped), and bull-types (YBULL, young male calves; CBULL, young candidate bulls; and PBULL, proven bulls). Results: The r_M1 estimates in the study were between 0.90 and 0.96 among five traits. The r_M1 estimates varied slightly by population and info-type, but noticeably by bull-type for traits. Generally average r_M2 estimates were much smaller than r_M1 (pedBLUP, 0.40 to0.44; ssGBLUP, 0.41 to 0.45) at population level. However, r_M2 from both BLUP models varied noticeably across info-types and bull-types. The ssGBLUP estimates of r_M2 in PHEN, GEN, and PH+ GEN ranged between 0.51 and 0.63, 0.66 and 0.70, and 0.68 and 0.73, respectively. In YBULL, CBULL, and PBULL, the r_M2 estimates ranged between 0.54 and 0.57, 0.55 and 0.62, and 0.70 and 0.74, respectively. The pedBLUP based r_M2 estimates were also relatively lower than ssGBLUP estimates. At the population level, we found an increase in accuracy by 2.0% to 4.5% among traits. Traits in PHEN were least influenced by ssGBLUP (0% to 2.0%), whereas the highest positive changes were in GEN (8.1% to 10.7%). PH+GEN also showed 6.5% to 8.5% increase in accuracy by ssGBLUP. However, the highest improvements were found in bull-types (YBULL, 21% to 35.7%; CBULL, 3.3% to 9.3%; PBULL, 2.8% to 6.1%). Conclusion: A noticeable improvement by ssGBLUP was observed in this study. Findings of differential responses to ssGBLUP by various bulls could assist in better selection decision making as well. We, therefore, suggest that ssGBLUP could be used for GS in Hanwoo proven-bull evaluation program.

• Asian-Australasian Journal of Animal Sciences
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• v.32 no.11
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• pp.1657-1663
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• 2019

Objective: A genome-based best linear unbiased prediction (GBLUP) method was applied to evaluate accuracies of genomic estimated breeding value (GEBV) of carcass and reproductive traits in Berkshire, Duroc and Yorkshire populations in Korean swine breeding farms. Methods: The data comprised a total of 1,870, 696, and 1,723 genotyped pigs belonging to Berkshire, Duroc and Yorkshire breeds, respectively. Reference populations for carcass traits consisted of 888 Berkshire, 466 Duroc, and 1,208 Yorkshire pigs, and those for reproductive traits comprised 210, 154, and 890 dams for the respective breeds. The carcass traits analyzed were backfat thickness (BFT) and carcass weight (CWT), and the reproductive traits were total number born (TNB) and number born alive (NBA). For each trait, GEBV accuracies were evaluated with a GEBV BLUP model and realized GEBVs. Results: The accuracies under the GBLUP model for BFT and CWT ranged from 0.33-0.72 and 0.33-0.63, respectively. For NBA and TNB, the model accuracies ranged 0.32 to 0.54 and 0.39 to 0.56, respectively. The realized accuracy estimates for BFT and CWT ranged 0.30 to 0.46 and 0.09 to 0.27, respectively, and 0.50 to 0.70 and 0.70 to 0.87 for NBA and TNB, respectively. For the carcass traits, the GEBV accuracies under the GBLUP model were higher than the realized GEBV accuracies across the breed populations, while for reproductive traits the realized accuracies were higher than the model based GEBV accuracies. Conclusion: The genomic prediction accuracy increased with reference population size and heritability of the trait. The GEBV accuracies were also influenced by GEBV estimation method, such that careful selection of animals based on the estimated GEBVs is needed. GEBV accuracy will increase with a larger sized reference population, which would be more beneficial for traits with low heritability such as reproductive traits.

• Animal Bioscience
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• v.37 no.4
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• pp.555-566
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• 2024

Objective: This study aimed to assess the genetic parameters and accuracy of genomic predictions for twenty-four linear body conformation traits and overall conformation scores in Korean Holstein dairy cows. Methods: A dataset of 2,206 Korean Holsteins was collected, and genotyping was performed using the Illumina Bovine 50K single nucleotide polymorphism (SNP) chip. The traits investigated included body traits (stature, height at front end, chest width, body depth, angularity, body condition score, and locomotion), rump traits (rump angle, rump width, and loin strength), feet and leg traits (rear leg set, rear leg rear view, foot angle, heel depth, and bone quality), udder traits (udder depth, udder texture, udder support, fore udder attachment, front teat placement, front teat length, rear udder height, rear udder width, and rear teat placement), and overall conformation score. Accuracy of genomic predictions was assessed using the single-trait animal model genomic best linear unbiased prediction method implemented in the ASReml-SA v4.2 software. Results: Heritability estimates ranged from 0.10 to 0.50 for body traits, 0.21 to 0.35 for rump traits, 0.13 to 0.29 for feet and leg traits, and 0.05 to 0.46 for udder traits. Rump traits exhibited the highest average heritability (0.29), while feet and leg traits had the lowest estimates (0.21). Accuracy of genomic predictions varied among the twenty-four linear body conformation traits, ranging from 0.26 to 0.49. The heritability and prediction accuracy of genomic estimated breeding value (GEBV) for the overall conformation score were 0.45 and 0.46, respectively. The GEBVs for body conformation traits in Korean Holstein cows had low accuracy, falling below the 50% threshold. Conclusion: The limited response to selection for body conformation traits in Korean Holsteins may be attributed to both the low heritability of these traits and the lower accuracy estimates for GEBVs. Further research is needed to enhance the accuracy of GEBVs and improve the selection response for these traits.