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.