Applying an appropriate statistical analysis is complementary for conducting a robust experimental design in plant and animal breeding. In these experiments 33 Iranian bread wheat genotypes, cultivated in a randomized complete blocks design with three replications in two normal and saline conditions were evaluated at the field of National Salinity Research Center located in Yazd province, Iran. The restricted maximum likelihood (REML) was used to evaluate the different genotypic variance-covariance structures and to estimate the genotypic and phenotypic correlations of some of Iranian wheat traits under two normal and salt-stressed conditions. The Using different estimation by REML method the traits of grain yield, biological yield and harvest index had different and significant values across two conditions, this genetic variability can be used for salinity tolerance of bread wheat in breeding programs.. In addition, genotype by environment interaction for all traits was not significant, especially for grain yield as important trait for evaluation of salinity tolerance in wheat. The means comparisons of genotypes showed that the SALT22, SALT29 and SALT28 had the highest values and line No. 6, Shahpasand and line No.13 had the lowest values for grain yield, respectively. There were significantly positive genetic correlation between yield with biological yield (0.97) and harvest index (0.94) in combined analysis and negative genetic correlation for days to maturity with grain yield (-0.32) in saline condition by REML estimator. So, the selection of early maturing genotypes with higher yield in the saline condition, especially in the location of conducted experiment (Yazd) is achievable and selection can be done to improve the performance of salinity stress.

In order to estimation genotypic correlation and heritability of some faba bean traits, 26 faba bean genotypes were evaluated in a randomized complete block design with three replications during 2014-16 growing seasons in Agricultural Research Sation of Borujerd located in Lorestan province, Iran. The restricted maximum likelihood (REML) was used to estimate the genotypic and phenotypic correlations, broad sence heritability and genetic gain. Analysis of variance based on least squares and REML indicated significant effect of genotype on days to maturity, plant height, hundred seed weight, pod length and dry seed yield. Genotype×year interactions were significant on all of the traits except of pod length. Borujerd cultivar (G26) and G20 had the highest dry seed yield in both of years. REML results indicated a significant positive genetic correlation between dry seed yield and biological yield and plant height. Also, there were a significant negative phenotypic correlation between dry seed yield and days to maturity, and significant positive phenotypic correlation between dry seed yield and plant height, biological yield and harvest index. So, the selection of early maturing genotypes with a higher yield is achievable and selection can be done to improve the performance of dry seed yield. Cluster analysis indicated variability among genotypes. According to values of broad sence heritability and genetic gain for plant height and high genetic correlation of this trait and dry seed yield; plant height can be used as a suitable trait for improving dry seed yield by selection.

Accurate estimation of variance components using pedigree and genomic data plays a key role in prediction of breeding values. Since SNP markers in genomic selection are distributed across the genome, they may cover all quantitative traits loci and potentially explain all of genetic variation. In this study, genotype data from Merino sheep, genotyped by 50k Illumina SNP chip were used. Staple length and Fibre diameter traits were studied in this research. To study the association between allele frequency spectrum and captured additive genetic variance, all SNPs were partitioned in five MAF bins with the equal numbers of SNPs. Two statistical models including separate analysis for each category of MAF SNPs or joint analysis of all MAF groups were fitted. The analysis were performed using REML (parametric) and a Bayesian method implemented via Gibbs sampling and RKHS (semi-parametric) model. Using all common SNPs in REML approach, estimates of genomic heritability were 0. 72 and 0. 48 for Staple length and Fibre diameter, respectively. In Bayesian approach, genomic heritability for mentioned traits were 0. 74 and 0. 47 respectively. In the separate analysis, estimates of genomic heritability using REML and Bayesian approaches for each MAF class were similar, but in joint analysis estimates of two approaches were different. Overall, when the model is simple both approaches perform similarly while when model is complicated as joint analysis in present study, two approaches work different. Therefore, to determine which approach is more reliable, further research is required

The Restricted Mean Survival Time (RMST) serves as a valuable and extensively utilized metric in clinical trials. However, its application becomes intricate when dealing with data affected by length-biased sampling, rendering traditional inference strategies inadequate. To overcome this challenge, we advocate for the adoption of nonparametric techniques. One notably promising approach is the Empirical Likelihood (EL) method, which furnishes robust results without the need for stringent parametric assumptions. In practical scenarios, the underlying sampling distributions often remain elusive, necessitating adjustments in the case of parametric methodologies. The EL method has demonstrated its efficacy in addressing such complexities. Consequently, this paper introduces the EL method for computing RMST in situations involving both length-biased and right-censored data. Additionally, we introduce the concept of adjusted empirical likelihood (AEL) to further enhance the coverage probability, particularly when dealing with smaller sample sizes. To gauge the performance of the EL and AEL methods, we conduct simulations and rigorously compare their results. The findings unequivocally demonstrate that AEL-based confidence intervals consistently provide superior coverage probability when juxtaposed with EL-based intervals. Lastly, we substantiate the practical applicability of our proposed method by employing it in the analysis of a real dataset.

In this paper, we first introduce semi-parametric heteroscedastic hierarchical models. Then, we define a new version of the empirical likelihood function (Restricted Joint Empirical likelihood) and use it to obtain the shrinkage estimators of the models' parameters in these models. Under different assumptions, a simulation study investigates the better performance of the restricted joint empirical likelihood function in the analysis of semi-parametric heterogeneity hierarchical models. Furthermore, we analyze an actual data set using the RJEL method.

The restricted mean survival time (RMST) in the context of length-biased data is an important addition to clinical studies. The RMST is a widely used measurement for evaluating survival over a specific period, and the area under the survival function is a key component of this metric. However, when the data under study are length-biased, traditional parametric and classical methods for examining the RMST are not applicable. Nonparametric and semi-parametric methods are used to address this issue. We utilize the empirical likelihood (EL) method to investigate RMST.Our proposed EL procedure provides a reliable approach for inferential analysis of RMST in the presence of length-biased data. We have shown that the limiting distribution of the empirical log-likelihood ratio is a chi-square distribution with one degree of freedom. We also demonstrated that the likelihood ratio exhibits weak convergence to a mean-zero Gaussian process, which we used to construct a confidence band.In our simulation section, we compared the confidence intervals obtained from the normal approximation (NA) and EL methods. We showed that the EL method has a better coverage probability than the NA method. Additionally, we provided a real data application using bank customers' monthly taxes to illustrate further the effectiveness of our proposed method.

To conduct any breeding program, understanding of the genetic structure of traits and effect of environment and genetic by environment interaction as well as effects of random or fixed in the analysis of results is essential. Subsequently, analysis of variances and variance components are important in plant and animal breeding. The ANOVA is one of the best estimators for variance components. But this estimator is not preferred to maximum likelihood (ML) and Restricted Maximum Likelihood (REML) methods when variance components are negatively estimated and unbalanced datasets arise. Therefore, the objective of this research is a review of comparison of estimates of variance components using ANOVA, ML and REML method in linear mixed models using experimental data.

In the present research, performance records of Fars native chicken from years 1988 to 2002 were used. Studied traits were body weight at 12 weeks (BW12), age at sexual maturity (ASM) egg weight (EW) and egg number (EN). Variance Components and genetic, phenotype and environmental correlations were estimated using restriction maximum likelihood (REML) and Bayesian analysis method based on Gibbs sampling technique under univariate and multivariate animal model. Univariate estimation of heritabilities with REML for ASM, EW, EN and BW12 were 0.53, 0.63, 0.33 and 0.53, while, with multivariate model these values were 0.51, 0.64, 0.33 and 0.53, respectively.Heritabilities estimates with Bayesian analysis in univariate model for ASM, EW, EN and BW12 were 0.53, 0.63, 0.34 and 0.55, respectively, while with multivariate model were these values 0.56, 0.58, 0.33 and 0.55, respectively. Genetic and environmental correlations between BW12 and ASM using both methods were negative but phenotypic correlation was positive. Genetic, environmental and phenotypic correlations between BW12 and EW and EN with both methods were positive. The estimates between W12 and EW with REML were 0.5, 0.15 and 0.36, whereas with Bayesian were 0.43, 0.26 and 0.28, respectively. Those estimates between BW12 and EN with REML were 0.03, 0.15 and 0.1, respectively, whereas with Bayesian were 0.19, 0.23 and 0.19, respectively. The above mentioned correlations between ASM and EN were high and negative using both methods. It can be concluded that the estimation of the parameters evalvated using with these two methods are close together.

Background and objectives: The Markhoz goat is one of the most important breeds In Iran. These animals had an important cultural role in Kurdistan because the mohair obtained from these animals is used for making national clothes. The mating of related individuals produces an inbred offspring and leads to an increased homozygosity in the progeny, genetic variance decrease within families and increase between families. The ratio of homozygosity for individuals was calculated by inbreeding coefficient. The trend of inbreeding is an indicator for determination of inbreeding level in the herd. Result of researches showed increasing of inbreeding resulted to decrease of phenotypic value in some of production and reproduction traits. So the aims of this study were estimation of inbreeding coefficients and its effects on birth weight (BW), weaning weight (WW), average daily gain to weaning (ADG), 6 month weight (6MW), 9 month weight (9MW) and yearling weight (YW) of Markhoz goats.Materials and methods: In this study, pedigree data of 4186 Markhoz goats which were collected from 1992-2012 by Markhoz Goat breeding center located in Sanandaj, were used. Inbreeding coefficient was estimated by the CFC software program. Inbreeding depressions in growth traits were estimated by restricted maximum likelihood (REML) method under 12 animal models that animal and dam’s inbreeding coefficients added to models as a covariate. The most appropriate model for each trait was determined by Akaike’s information criterion (AIC).Results: The 58.07% of animal were inbred. The mean inbreeding coefficient for the herd and inbred population was 3.03 and 5.21% respectively. Maximum inbreeding coefficient was 31.25%. The 47.04% of animal was inbreeding coefficient between 0 to 10 percent.553 head of dams were inbred and inbreeding coefficient for the whole and inbred dams was 2.05 and 4.91% respectively. Inbreeding coefficient was increased 0.24±0.04 percent in each year (P<0.01). Inbreeding depression per 1 percent increase in individual inbreeding for BW, WW, ADG, 6MW, 9MW and YW were -0.5±1.57, -20.20±7.21, -0.11±0.13, -30.49±12.38, +9.49±17.87 and -58.67±24.40 gr, respectively. Inbreeding depression per 1 percent increase in dam inbreeding for these traits were -0.05±2.08, -6.62±9.74, -0.03±0.16, -13.90±9.76, -39.27±13.59 and -49.37±25.12 gr, respectively.Conclusion: Estimated inbreeding coefficients for this breed showed high degree of close mating in this flock and due to significant effect of inbreeding on some growth traits it is suggested that this breeding station should use a breeding plan to avoid mating of close relative animals.