广义最小二乘估计的稳健性

Robustness of GLSE

讨论了协方差阵未知的椭球等高线性模型中的稳健性问题．证明当协方差阵在一定范围内变动时,广义最小二乘估计在一大类损失函数下部是风险最小的估计;广义最小二乘估计关于协方差阵和损失函数同时具有稳健性．

Linear regression model with elliptically symmetric errors and unknown dispersion matrix was discussed. For a given matrix ∑0, when the real dispersion matrix varying within certain range, the GLSE β∑（∑0） = （X＇∑o^-1X）^-1X＇]E0^-1y is the minimum risk estimator under a large class of loss functions, which implies the GLSE is a robust estimator with respect to dispersion matrix and loss functions.