Study On The Relative Efficiency In Parameter Estimation For Linear Model

The mixed-coefficient linear model is one of the most important and applied models in the linear model,and an important branch of statistics. Because it is difficult or impossible for us to get the best linear unbiased estimate(BLUE) for some reason, then the least square estimate(LSE) is widely used as a substitute for BLUE.But this alternative is not absolutely equivalent to the former, it probably change the results and reduce the precision,so a lot of scholars put forward relative efficiency of the least square estimate to the best linear unbiased estimate for the unknown parameter from different aspects. In recent years, increasingly, more scholars are discussing the relative efficiency and their corresponding nature linear model.In this paper, we gave a detailed account of the mixed-coefficient linear model and did the fundamental processing to the model. A diagonal matrix is introduced to converting the standard form of the model.This discussing some estimations in the linear mixed-coefficient linear model be given,such as LSE 、s-k estimate、s-k-b estimate、improved s-k-b estimate、improved ridge estimate and so on.On the basis, the estimated parameters in the model relative efficiency were studied to find some new relative efficiency. Firstly, we get relative efficiency by introducing the relative efficiency,as the same time,we find the relative efficiency between LSE and the modified ridge estimation. And prove some properties of the relative efficiency in this model when its bound is given. Secondly, another new relative efficiency in linear weighted regression model is proposed by using the sametheory. Then we proved some properties of this relative efficiency in this model besides giving its bound.