The Influence Analysis Of LIU Estimation In Restricted Linear Model

The research about least square estimation of regression parameters in the linear model has included integrated and systemic results. However, when there exists multiple correlation, the least squares estimate shows considerable instability. Statisticians have proposed to replace the linear biased estimate to unbiased estimate to solve this problem. In a biased study of the estimate, the ridge estimate is the most extensive.It overcomes the problem by adding a parameter K. However, when the multiple correlation problem is more series, the ridge estimate is not effective. The LIU estimate is a new two-parameter estimator presented by K.J.LIU. It can not only address the ill conditioning problem, but also have less mean squared error. This article mainly studies the influence analysis of LIU estimation in restricted linear model. Based on the proposed conditional LIU estimation, we analysis the influence of the three kinds of disturbance on the conditional LIU estimation, and give the relevant conclusions.This paper first introduces the basic research of linear model and impact analysis, introduces some basic knowledge of the matrix, LIU estimation and impact analysis and gives the generalized Cook distance to measure the degree of the influence. In the second, third, and fifth chapters, we study the influence analysis of the covariance matrix disturbance, data deleted disturbance and mean shift disturbance on the linear model with constraints, establish the relationships of the conditional LIU estimation between before disturbance and after disturbance and give the corresponding formulas of the generalized Cook distance. An example is given in the third chapter too.Finally the paper makes a summary and gives the proposed research problems and their prospects.