The Impact Analysis And Local Influence Analysis Of LIU Estimate In Linear Model

The least square estimation has been widely used in linear regression. However, when there exists multiple correlation among the variables, the least squares method shows considerable instability. To solve this problem, statisticians have proposed to re-place the linear biased estimate to unbiased estimate. In a biased study of the estimate, the ridge estimate is the most extensive. However, when the multicollinearity problem is more serious, the ridge estimator is not effective to overcome the multicollinearity. So, KJLIU presents a new biased estimate called LIU estimate. In the paper, we discuss the impact analysis and local influence of LIU estimate.This paper first outlines the impact of the linear model analysis and the basic re-search of local impact analysis. In the second chapter, we introduced some basic knowl-edge and theory of matrix, linear models, impact analysis and local impact analysis. In chapter three, we discussed the Cook distance of LIU estimate in the deletion model, variance disturbance model, estimated mean shift model, then we obtained the impact of LIU estimate. In chapter four, we used Shi Lei's method, the local influence of LIU estimated are discussed in disturbance model, variables disturbance model, then we verified the influence by numerical examples.