可估子空间上一般随机效应模型的比较  

Comparison of General Stochastic Effect Models in the Estimable Subspace

作　　者：彭萍[1] 吴志强[1] 胡桂开[1] 

机构地区：[1]东华理工大学数学与信息科学学院,江西抚州344000

出　　处：《东华理工大学学报（自然科学版）》2011年第1期97-100,共4页Journal of East China University of Technology(Natural Science)

基　　金：东华理工大学校长基金(DHXK0912)

摘　　要：对于具有已知对称非负定协方差阵的一般随机效应模型,通过比较回归系数和参数线性可估函数的最优线性无偏估计方差的大小,给出了一个随机效应模型至少与另一个随机效应模型一样好的定义,并在可估空间的子空间上对两个随机效应模型进行比较,通过利用矩阵的广义逆理论和方法,得到了一个随机效应模型至少与另一个随机效应模型一样好的充分必要条件,为统计建模过程中模型选择奠定了理论依据。The comparison of two stochastic effect models where covariance matrices are known and symmetric nonnegative definite is considered.The definition for one stochastic effect model to be at least as good as the other in comparing with variance of the best linear unbiased estimator of linear estimable function of regression coefficient and parameter is given.The necessary and sufficient conditions for one stochastic effect model to be at least as good as the other are obtained in the estimable subspace of linear function by using the generalized inverse of matrix.The theoretical basis can be determined by them for model selecting during statistical modeling.

关 键 词：随机效应模型 可估子空间 可估函数 

分 类 号：O212.4[理学—概率论与数理统计]