For a system of two seerningly umrelated regressions.some general results of mean square er-ror matrix comparisons are presented.A class of linear estimators and a class of two-stage estimatorsbased on a generalized u...For a system of two seerningly umrelated regressions.some general results of mean square er-ror matrix comparisons are presented.A class of linear estimators and a class of two-stage estimatorsbased on a generalized unrestricted estimate of the dispersion matrix are proposed.Some exact finitesample properties of the two-stage estimators are obtained.展开更多
In this paper, we propose a stochastic restricted s-K estimator in the linear model with additional stochastic linear restrictions by combining the ordinary mixed estimator （OME） with the s-K estimator. It is shown ...In this paper, we propose a stochastic restricted s-K estimator in the linear model with additional stochastic linear restrictions by combining the ordinary mixed estimator （OME） with the s-K estimator. It is shown that the proposed estimator is superior to the OME and the s-K estimator under the mean squared error matrix criterion under some conditions. Finally, a numerical example and a Monte Carlo simulation study are given to verify the theoretical results.展开更多
In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares...In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.展开更多
This paper investigates the optimal design problem for the prediction of the individual parameters in hierarchical linear models with heteroscedastic errors.An equivalence theorem is established to characterize D-opti...This paper investigates the optimal design problem for the prediction of the individual parameters in hierarchical linear models with heteroscedastic errors.An equivalence theorem is established to characterize D-optimality of designs for the prediction based on the mean squared error matrix.The admissibility of designs is also considered and a sufficient condition to simplify the design problem is obtained.The results obtained are illustrated in terms of a simple linear model with random slope and heteroscedastic errors.展开更多
In this paper,we propose a new biased estimator namely modified almost unbiased Liu estimator by combining almost unbiased Liu estimator(AULE)andridge estimator(RE)in a linear regression model when multicollinearity p...In this paper,we propose a new biased estimator namely modified almost unbiased Liu estimator by combining almost unbiased Liu estimator(AULE)andridge estimator(RE)in a linear regression model when multicollinearity presents amongthe independent variables.Necessary and sufficient conditions for the proposed estimator over the ordinary least square estimator,RE,AULE and Liu estimator(LE)in the mean squared error matrix sense are derived,and the optimal biasing parameters are obtained.To illustrate the theoretical findings,a Monte Carlo simulation study is carried out and a numerical example is used.展开更多
For the two-parameter inverse Gaussian distribution denoted by IG（μ,A）, the authors employ a linear Bayes procedure to estimate the parameters μ and A. The superiority of the proposed linear Bayes estimator （LBE...For the two-parameter inverse Gaussian distribution denoted by IG（μ,A）, the authors employ a linear Bayes procedure to estimate the parameters μ and A. The superiority of the proposed linear Bayes estimator （LBE） over both the classical UMVUE and the maximum likelihood estimator （MLE） is established in terms of the mean squared error matrix （MSEM） criterion. Compared with the usual Bayes estimator, which is obtained by an MCMC method, the proposed LBE is simple and easy to use. Some numerical results are presented to verify that the LBE performs well.展开更多
In this article,we propose a new biased estimator,namely stochastic restricted modified almost unbiased Liu estimator by combining modified almost unbiased Liu estimator(MAULE)and mixed estimator(ME)when the stochasti...In this article,we propose a new biased estimator,namely stochastic restricted modified almost unbiased Liu estimator by combining modified almost unbiased Liu estimator(MAULE)and mixed estimator(ME)when the stochastic restrictions are available and the multicollinearity presents.The conditions of supe-riority of the proposed estimator over the ordinary least square estimator,ME,ridge estimator,Liu estimator,almost unbiased Liu estimator,stochastic restricted Liu esti-mator and MAULE in the mean squared error matrix sense are obtained.Finally,a numerical example and a Monte Carlo simulation are given to illustrate the theoretical findings.展开更多
In this article, the Bayes linear unbiased estimation （BALUE） of parameters is derived for the partitioned linear model. The superiorities of the BALUE over ordinary least square estimator （LSE） are studied in ter...In this article, the Bayes linear unbiased estimation （BALUE） of parameters is derived for the partitioned linear model. The superiorities of the BALUE over ordinary least square estimator （LSE） are studied in terms of the Bayes mean square error matrix （BMSEM） criterion and Pitman closeness （PC） criterion.展开更多
基金Suppported in part by Henan Natural Setence Foundatron(004051300)
文摘For a system of two seerningly umrelated regressions.some general results of mean square er-ror matrix comparisons are presented.A class of linear estimators and a class of two-stage estimatorsbased on a generalized unrestricted estimate of the dispersion matrix are proposed.Some exact finitesample properties of the two-stage estimators are obtained.
基金Supported by the National Natural Science Foundation of China(Grant No.11201005)the Natural Science Foundation of Anhui Province(Grant No.1308085QA13)+1 种基金the Key Project of Distinguished Young Talents of Universities in Anhui Province(Grant No.2012SQRL028ZD)the Key Project of Natural Science Foundation of Universities in Anhui Province(Grant No.KJ2012A135)
文摘In this paper, we propose a stochastic restricted s-K estimator in the linear model with additional stochastic linear restrictions by combining the ordinary mixed estimator （OME） with the s-K estimator. It is shown that the proposed estimator is superior to the OME and the s-K estimator under the mean squared error matrix criterion under some conditions. Finally, a numerical example and a Monte Carlo simulation study are given to verify the theoretical results.
基金the Knowledge Innovation Program of the Chinese Academy of Sciences(KJCX3-SYW-S02)the Youth Foundation of USTC
文摘In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.
基金supported by NSFC Grant(11871143,11971318)the Fundamental Research Funds for the Central UniversitiesShanghai Rising-Star Program(No.20QA1407500).
文摘This paper investigates the optimal design problem for the prediction of the individual parameters in hierarchical linear models with heteroscedastic errors.An equivalence theorem is established to characterize D-optimality of designs for the prediction based on the mean squared error matrix.The admissibility of designs is also considered and a sufficient condition to simplify the design problem is obtained.The results obtained are illustrated in terms of a simple linear model with random slope and heteroscedastic errors.
文摘In this paper,we propose a new biased estimator namely modified almost unbiased Liu estimator by combining almost unbiased Liu estimator(AULE)andridge estimator(RE)in a linear regression model when multicollinearity presents amongthe independent variables.Necessary and sufficient conditions for the proposed estimator over the ordinary least square estimator,RE,AULE and Liu estimator(LE)in the mean squared error matrix sense are derived,and the optimal biasing parameters are obtained.To illustrate the theoretical findings,a Monte Carlo simulation study is carried out and a numerical example is used.
基金supported by National Natural Science Foundation of China under Grant No.11371051
文摘For the two-parameter inverse Gaussian distribution denoted by IG（μ,A）, the authors employ a linear Bayes procedure to estimate the parameters μ and A. The superiority of the proposed linear Bayes estimator （LBE） over both the classical UMVUE and the maximum likelihood estimator （MLE） is established in terms of the mean squared error matrix （MSEM） criterion. Compared with the usual Bayes estimator, which is obtained by an MCMC method, the proposed LBE is simple and easy to use. Some numerical results are presented to verify that the LBE performs well.
文摘In this article,we propose a new biased estimator,namely stochastic restricted modified almost unbiased Liu estimator by combining modified almost unbiased Liu estimator(MAULE)and mixed estimator(ME)when the stochastic restrictions are available and the multicollinearity presents.The conditions of supe-riority of the proposed estimator over the ordinary least square estimator,ME,ridge estimator,Liu estimator,almost unbiased Liu estimator,stochastic restricted Liu esti-mator and MAULE in the mean squared error matrix sense are obtained.Finally,a numerical example and a Monte Carlo simulation are given to illustrate the theoretical findings.
基金This research is supported by National Natural Science Foundation of China under Grant Nos. 10801123, 10801124 and 10771204, and the Knowledge Innovation Program of the Chinese Academy of Sciences under Grant No. KJCX3-SYW-S02.
文摘In this article, the Bayes linear unbiased estimation （BALUE） of parameters is derived for the partitioned linear model. The superiorities of the BALUE over ordinary least square estimator （LSE） are studied in terms of the Bayes mean square error matrix （BMSEM） criterion and Pitman closeness （PC） criterion.
