Study On Parameter Estimation In The Mixed-coefficient Linear Model

In this paper, we mainly study the improvement problem of the parameter estimation in the mixed-coefficient linear model and the mixed-coefficient linear model with constraint. For the mixed-coefficient linear model, we propose the generalized ridge estimator and the improved ridge estimator (i.e., s-K estimator). For the constrained mixed-coefficient linear model, we propose the conditional ridge estimator. In addition, we investigate the superiority of the proposed estimators.The paper is divided into four chapters. 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, the generalized least squared estimator d and the generalized ridge estimator d(K) are introduced, and the corresponding properties are discussed.In the third chapter, we propose a new class of estimators which is called s-K estimator. Also, we study some properties of s-K estimator.In last chapter, the conditional ridge estimator in the constrained mixed-coefficient linear model is proposed.