On Biased Estimate Methods For Mixed-coefficient Liner Models

In this paper. we mainly study the improvement problem of the biased estimation mixed-coefficient linear model. The main results of this paper are as follows:In the first chapter, we review the development of the parameter estimation in the mixed-coefficient linear model. Moreover, we introduce some preliminary knowledge.In the second chapter, we proposed a new class of estimators which is called p-k estimator by combining the ridge estimator and root estimator. The superiority of the new estimator over the ridge estimator and the root estimator are discussed with respect to the mean squared error criterion. In addition, sufficient and necessary conditions for the p-k estimator being better than the OLS estimator in the mean square matrix sense.In the three chapter, the local s-k estimator and almost unbiased s-k estimator are intro-duced. Also, we study some properties of two kinds of estimators in the mean squared error and mean squared matrix sense...