Balanced Ridge Estimator Of Coefficient Parameter In Linear Statistical Model

This paper mainly studies the balanced ridge estimation of the coefficient parameters of the linear statistical model,and proves that the proposed balanced ridge estimation is superior to the least square estimation by comparison,and relies on various properties of the existing biased estimation.The practical significance behind the theory of deep excavation makes great efforts to push forward the research of ridge estimation in depth.This paper is divided into four parts.The first part is the introduction.In this part,the development history of least square estimation,biased estimation and the research status of equilibrium loss function at home and abroad are introduced.Secondly,it introduces the related theories and concepts of matrix,the differential of matrix,the mean square error,the properties of generalized inverse matrix and Moore-Penrose generalized inverse matrix.These theorems play a key role in the later argumentation.The mean deviation degree of the mean square error measure estimate and the complex collinearity make the least square estimation no longer ideal.Again,the correlation property of regression coefficient under equilibrium loss is introduced.The least square estimation is the basis of other biased estimators.When the design matrix has complex collinearity,the ridge estimation is the most widely used in the biased estimation.Loss can not be avoided in statistical decision making.Based on the thought of equilibrium loss,the expression of equilibrium least square estimation is derived,and the admissibility of linear admissible estimation of regression coefficient under equilibrium loss and linear estimation in singular linear model is introduced.The last part is the core of this paper,which mainly studies the related properties of ridge estimation under equilibrium loss,starting from the risk function of equilibrium loss function,because of the design matrix discussed in this paper.Therefore,any estimable function can be expressed as a linear function,so it is only necessary to discuss the good and admissible of the balanced ridge estimator of the estimable function.In this paper,the equilibrium loss function is constructed,and the concept of linear model coefficient parameter balanced ridge estimation is given.In the sense of estimable function,the singular value decomposition theorem,the differential and consistency of matrix are used.By comparing with the least square estimator,the admissibility and superiority of the balanced ridge estimator for the coefficient parameters of the linear statistical model are discussed.