In this paper, we derive the distributions of concomitants of record values from generalized Farlie-Gumbel-Morgenstern family of bivariate distributions. We derive the single and the product moments of the concomitant...In this paper, we derive the distributions of concomitants of record values from generalized Farlie-Gumbel-Morgenstern family of bivariate distributions. We derive the single and the product moments of the concomitants for the general case. The results are then applied to the ease of the two-parameter exponential marginal distributions. Using concomitants of record values we derive the best linear unbiased estimators of parameters of the marginal distributions. Moreover, two methods for obtaining predictors of concomitants of record values are presented. Finally, a numerical illustration is performed to highlight the theoretical results obtained.展开更多
Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class c...Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class correlation of residual errors and the group sizes are equal. Specifically: 1) How does the variance of the generalized least squares (GLS) estimator (GLSE) depend on the regressor values? 2) What is the bias in estimated variances when ordinary least squares (OLS) estimator is used? 3) In what cases are OLS and GLS equivalent. 4) How can the best linear unbiased estimator (BLUE) be constructed when the covariance matrix is singular? The purpose is to make general matrix results understandable. Results: The effects of the regressor values can be expressed in terms of the intra-class correlations of the regressors. If the intra-class correlation of residuals is large, then it is beneficial to have small intra-class correlations of the regressors, and vice versa. The algebraic presentation of GLS shows how the GLSE gives different weight to the between-group effects and the within-group effects, in what cases OLSE is equal to GLSE, and how BLUE can be constructed when the residual covariance matrix is singular. Different situations arise when the intra-class correlations of the regressors get their extreme values or intermediate values. The derivations lead to BLUE combining OLS and GLS weighting in an estimator, which can be obtained also using general matrix theory. It is indicated how the analysis can be generalized to non-equal group sizes. The analysis gives insight to models where between-group effects and within-group effects are used as separate regressors.展开更多
Grain size plays a significant role in rice,starting from affecting yield to consumer preference,which is the driving force for deep investigation and improvement of grain size characters.Quantitative inheritance make...Grain size plays a significant role in rice,starting from affecting yield to consumer preference,which is the driving force for deep investigation and improvement of grain size characters.Quantitative inheritance makes these traits complex to breed on account of several alleles contributing to the complete trait expression.We employed genome-wide association study in an association panel of 88 rice genotypes using 142 new candidate gene based SSR(cgSSR)markers,derived from yield-related candidate genes,with the efficient mixed-model association coupled mixed linear model for dissecting complete genetic control of grain size traits.A total of 10 significant associations were identified for four grain size-related characters(grain weight,grain length,grain width,and length-width ratio).Among the identified associations,seven marker trait associations explain more than 10%of the phenotypic variation,indicating major putative QTLs for respective traits.The allelic variations at genes OsBC1L4,SHO1 and OsD2 showed association between 1000-grain weight and grain width,1000-grain weight and grain length,and grain width and length-width ratio,respectively.The cgSSR markers,associated with corresponding traits,can be utilized for direct allelic selection,while other significantly associated cgSSRs may be utilized for allelic accumulation in the breeding programs or grain size improvement.The new cgSSR markers associated with grain size related characters have a significant impact on practical plant breeding to increase the number of causative alleles for these traits through marker aided rice breeding programs.展开更多
文摘In this paper, we derive the distributions of concomitants of record values from generalized Farlie-Gumbel-Morgenstern family of bivariate distributions. We derive the single and the product moments of the concomitants for the general case. The results are then applied to the ease of the two-parameter exponential marginal distributions. Using concomitants of record values we derive the best linear unbiased estimators of parameters of the marginal distributions. Moreover, two methods for obtaining predictors of concomitants of record values are presented. Finally, a numerical illustration is performed to highlight the theoretical results obtained.
文摘Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class correlation of residual errors and the group sizes are equal. Specifically: 1) How does the variance of the generalized least squares (GLS) estimator (GLSE) depend on the regressor values? 2) What is the bias in estimated variances when ordinary least squares (OLS) estimator is used? 3) In what cases are OLS and GLS equivalent. 4) How can the best linear unbiased estimator (BLUE) be constructed when the covariance matrix is singular? The purpose is to make general matrix results understandable. Results: The effects of the regressor values can be expressed in terms of the intra-class correlations of the regressors. If the intra-class correlation of residuals is large, then it is beneficial to have small intra-class correlations of the regressors, and vice versa. The algebraic presentation of GLS shows how the GLSE gives different weight to the between-group effects and the within-group effects, in what cases OLSE is equal to GLSE, and how BLUE can be constructed when the residual covariance matrix is singular. Different situations arise when the intra-class correlations of the regressors get their extreme values or intermediate values. The derivations lead to BLUE combining OLS and GLS weighting in an estimator, which can be obtained also using general matrix theory. It is indicated how the analysis can be generalized to non-equal group sizes. The analysis gives insight to models where between-group effects and within-group effects are used as separate regressors.
基金supported by Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(10XNL018)Project of Humanities Social Science Foundation of Hubei Provincial Department of Education(2012G078)
基金ICAR-National Rice Research Institute for financial support
文摘Grain size plays a significant role in rice,starting from affecting yield to consumer preference,which is the driving force for deep investigation and improvement of grain size characters.Quantitative inheritance makes these traits complex to breed on account of several alleles contributing to the complete trait expression.We employed genome-wide association study in an association panel of 88 rice genotypes using 142 new candidate gene based SSR(cgSSR)markers,derived from yield-related candidate genes,with the efficient mixed-model association coupled mixed linear model for dissecting complete genetic control of grain size traits.A total of 10 significant associations were identified for four grain size-related characters(grain weight,grain length,grain width,and length-width ratio).Among the identified associations,seven marker trait associations explain more than 10%of the phenotypic variation,indicating major putative QTLs for respective traits.The allelic variations at genes OsBC1L4,SHO1 and OsD2 showed association between 1000-grain weight and grain width,1000-grain weight and grain length,and grain width and length-width ratio,respectively.The cgSSR markers,associated with corresponding traits,can be utilized for direct allelic selection,while other significantly associated cgSSRs may be utilized for allelic accumulation in the breeding programs or grain size improvement.The new cgSSR markers associated with grain size related characters have a significant impact on practical plant breeding to increase the number of causative alleles for these traits through marker aided rice breeding programs.
基金supported by the National Natural Science Foundation of China(11326066)the Doctoral Program of Shandong Province(BS2013SF011)+1 种基金the Shandong Province Higher Education Science and Technology Program(J14LI01)the Key Project of Scientific Research Innovation Foundation of Shanghai Municipal Education Commission(13ZZ080)
