Linear Minimax Estimation Of The Two Linear Models Of Regression Coefficients Under The Quadratic Loss

In this paper, we recall the preliminary of linear models theory and mainly discuss the minimax estimator problems in statistical decision theory. We study the minimax estimator and maximum risk under quadric loss in restricted linear models and unrestricted linear models respectively.First, the notion of linear condition minimax estimator of regression coefficient under quadric loss in unrestricted linear models is defined and some basic properties of such minimax estimator are also presented. Moreover, the unique linear conditional minimax estimator of regression coefficient and the expression of its maximum risk function are eventually given. Next, we obtain some basic properties of the linear condition minimax estimator of regression coefficient under quadric loss in restricted linear models. Also, the unique linear conditional minimax estimator of regression coefficient and the expression of its maximum risk function in restricted linear models are eventually given.