Fay-Herriot模型中两步估计的均方误差矩阵  

Mean Squared Error Matrix of Two-Stage Estimete in Fay-Herriot Model

作　　者：叶仁道[1] 王松桂[2] 

机构地区：[1]杭州电子科技大学财经学院,杭州310018 [2]北京工业大学应用数理学院,北京100124

出　　处：《数学学报（中文版）》2009年第2期315-322,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学数学天元青年基金(10726045);北京市属市管高等学校人才强教计划(0506011200702);杭州电子科技大学科研启动基金(KYS025608094)

摘　　要：在文献中,回归系数的两步估计是通过在最佳线性无偏估计中用方差参数的估计量取代方差参数来获得的.本文考虑了Fay-Herriot模型中两步估计的均方误差矩阵问题.当方差分量倒数的估计量是基于普通最小二乘残差时,建立了两步估计的均方误差矩阵和估计量偏差之间的直接关系.此外,给出了两步估计的均方误差矩阵的界.最后,把上面的结果推广到估计量不是基于普通最小二乘残差的一般条件下.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.

关 键 词：Fay—Herriot模型 均方误差矩阵 两步估计 

分 类 号：O212.1[理学—概率论与数理统计]