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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.