Linear Affine Estimation in Misspecified Linear Regression Models Using Fuzzy Prior Information

Within the framework of a possibly misspecified linear regression model, a generalized minimax approach is presented in order to determine an optimal linear affine estimator of the regression coefficient β. We make use of some fuzzy prior knowledge about β, about the misspecification and about the covariance structure. Here, the objective functions are based on the weighted mean squared error criterion. In case of symmetric prior information sets the optimization problem is, in essence, reduced to the linear term of the estimator. An application to ellipsoidal fuzzy constraints is given, and it is shown that an affine version of the generalized least squares estimator is optimal with respect to a large class of objective functions when there is no information available about β.