Influence Analysis And Local Influence Analysis Of Constrained LIU Estimation

Regression diagnosis is a very important issue in statistical research,and one of the main research contents is influence analysis and local influence analysis.In this paper,aiming at the linear model with additional information of equality constraint,the influence analysis and local influence analysis of constrained LIU estimation in linear regression model with equality constraint under several disturbances are studied.According to the influence analysis of constrained LIU estimation,the relationship between the original model and the disturbed model constrained LIU estimation under data deletion disturbance,mean shift disturbance and covariance matrix disturbance is obtained,and the generalized Cook distance statistics for diagnosing the influence of the three disturbances are given.At the same time,through an example,based on the theoretical research results,the influence analysis of constrained LIU estimation under data deletion disturbance and mean shift disturbance is discussed.The comparative analysis results show that the generalized Cook distance under data deletion disturbance and mean shift disturbance can effectively identify the influence points.According to the local influence analysis of constrained LIU estimation,the relationship between constrained LIU estimation and constrained LIU estimation under the original model when the variance of an independent variable,a dependent variable or a component of the dependent variable in the linear model with equality constraint is disturbed,and the generalized influence function and generalized Cook distance expressions under three disturbances are obtained.At the same time,based on generalized influence function and generalized Cook distance,the main diagnostic statistics under three different disturbances are given and the local influence analysis is carried out.Finally,through an example,based on the theoretical research results,the local influence analysis of three kinds of disturbances is analyzed and illustrated,and the effectiveness of the proposed method in identifying the influence points under three kinds of disturbances is discussed through comparative analysis.