THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL

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.

D-Optimal Designs for Hierarchical Linear Models with Heteroscedastic Errors

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.

THE SUPERIORITIES OF BAYES LINEAR UNBIASED ESTIMATION IN PARTITIONED LINEAR MODEL

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.

Modified Almost Unbiased Liu Estimator in Linear Regression Model

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.

Linear Bayes Estimators Applied to the Inverse Gaussian Lifetime Model

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.

On the Stochastic Restricted Modified Almost Unbiased Liu Estimator in Linear Regression Model

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.