Two New Relative Efficiencies of Linear Weighted Regression

In statistics parameter theory, usually the parameter estimations have two kinds,one is the least-square estimation(LSE),and the other is the best linear unbiased estimation (BLUE).Due to the determining theorem of minimum variance unbiased estimator(MVUE),the parameter estimation of BLUE in linear model is most ideal.But since the calculations are complicated or the covariance is not given,people are hardly to get the solution.Therefore people prefer to use LSE rather than BLUE.And this substitution will take some losses.To quantize the losses,many scholars have presented many kinds of different relative efficiencies in different views.For the linear weighted regression model, this paper discusses the relative efficiencies of LSE of β to BLUE of β. It also defines two new relative efficiencies and gives their lower bounds. Keywords—Linear weighted regression, Relative efficiency, Lower bound, Parameter estimation