方差分量模型中线性估计的最优性及可容许性

将随机效应线性模型和方差分量模型合并为一种模型,即具有随机回归系数的方差分量模型;给出了随机回归系数和参数的线性可估函数的最优线性无偏估计以及在矩阵损失函数下的可容许性;在正态假设下,讨论了线性估计在一切估计类中的可容许性.

The optimization and admissibility of the linear estimator in the variance components model with stochastic regression coefficients

This paper combines the variance components model with the stochastic effect model, and the new model is called the variance components model with stochastic regression coefficients. The minimum variance unbiased estimate of stochastic regression coefficients and parameters were obtained.Necessary and sufficient conditions for a linear estimators o stochastic regression coefficients and parameters to be admissible among the linear estimators under the quadratic loss function and matrix loss function are obtained respectively.Under normality assumption, the admissibility of the linear estimator among all the estimators are also discussed.