Research On Local Influence Analysis Of Modified Ridge-type Estimation In Linear Model

Regression diagnosis is an important content of data analysis.In many researches on regression diagnosis,the detection of influence points has always been the key and hot topic.In this thesis,we mainly study the influence point detection of the modified Ridge-type estimator in linear models based on two kinds of local impact analysis methods.Local influence analysis of the modified Ridge-type estimator based on likelihood distance method.Firstly,the extended model of the modified Ridge-type regression model is established,and the likelihood function and maximum likelihood estimator of the extended model are obtained.Secondly,the variance,response variables and explanatory variables of the enlarged model are perturbated,and the statistics used to detect the influence points under the three perturbation schemes are derived based on the Cook likelihood distance method and Tsai,Billor and Loynes(TBL)likelihood distance method.Finally,the validity of the method in this chapter is verified by empirical analysis.Local influence analysis of the modified Ridge-type estimator based on generalized influence function(GIF)and generalized Cook statistics(GC)is presented.First,the variance,response variables and single explanatory variables of the modified Ridge-type regression model are perturbated respectively.Then,the relations of the modified Ridge-type estimator before and after perturbation are derived for the three perturbation schemes.The generalized influence functions of the three perturbation schemes are obtained by using the relations,and two kinds of generalized Cook statistics are obtained by using different positive definite matrices.Finally,the theoretical results are empirically analyzed,and the results show that the identified influence points are roughly the same as previous studies.