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摘要: 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都是风险最小的估计; 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.
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关键词:
- 广义最小二乘估计 /
- Gauss-Markov定理 /
- 稳健性 /
- 同变估计 /
- 对称凸函数
Abstract: Linear regression model with elliptically symmetric errors and unknown dispersion matrix was discussed. For a given matrix $ \Sigma}_{0}$, when the real dispersion matrix varying within certain range, the GLSE $\hat{\beta}({\vec \Sigma}_{0}) = (\X'{\vec \Sigma}_{0}^{-1}\X)^{-1}\X'{\vec \Sigma}_{0}^{-1}y$ 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. -
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