Abstract:

The research that focuses on the robustness for the estimation of unknown parameters in the linear model has been a hot topic of statistics. In this paper, the robustness of Bayes linear unbiased estimator of the regression coefficients in the linear model in terms of error covariance and prior distributions are discussed, and the necessary and sufficient conditions for Bayes linear unbiased estimator holding its optimality when error covariance varies, or prior distributions vary, or error covariance and prior distributions vary, are respectively obtained.

Key words: linear model; Bayes linear unbiased estimator; robustness; prior distribution