School of Finance and Statistics, East China Normal University; Key Laboratory of Data Analyzing and Image Processing, Department of Mathematics and Finance, Chongqing University of Arts and Sciences

In this paper, the best linear unbiased estimator of
regression coefficients in the linear model is studied. Under weighted balanced
loss function the minimum risk properties of linear estimator of regression
coefficients in the class of linear unbiased estimator is discussed. Furthermore,
some kinds of relative efficiencies of the best linear unbiased estimator and
ordinary least squares estimator are given, and the lower bound or upper bound
of these relative efficiencies are also given.