Mean Squared Error Matrix of Two-Stage Estimete in Fay-Herriot Model
Ren Dao YE College of Business,Hangzhou Dianzi University,Hangzhou 310018,P.R.China Song Gui WANG College of Applied Sciences,Beijing University of Technology,Beijing 100124,P.R.China
In the literature,a two-stage estimate of regression coefficients is obtained by replacing the variance parameters with their estimators in the best linear unbiased estimator.In this paper,we consider the problem of mean squared error matrix of two-stage estimate in Fay-Herriot model.When the estimator for the reciprocal of variance component is based on the ordinary least square residual,we set up the direct relationship between the mean squared error matrix of two-stage estimate and bias of estimator.In addition,a bound for the mean squared error matrix of two-stage estimate is given.Finally,the above results are extended under the general conditions where the estimator may be not based on the ordinary least square residual.
Ren Dao YE College of Business,Hangzhou Dianzi University,Hangzhou 310018,P.R.China Song Gui WANG College of Applied Sciences,Beijing University of Technology,Beijing 100124,P.R.China.
Mean Squared Error Matrix of Two-Stage Estimete in Fay-Herriot Model. Acta Mathematica Sinica, Chinese Series, 2009(02): 109-116 https://doi.org/10.12386/A2009sxxb0037