Further Exploration On The Linear Regression Model Parameters Biased Estimate

Linear Statistical models mainly include Linear Regression model, variance and analysis model,Covariance and analysis model etc..This paper mainly discuss GeneralizedLinear regression model,accordingly,In term of the unknown parameterβ,it is necessary to study the estimation ofβand its linear function.when the design matrix X ill-conditions,we find the least squares estimator can be not a good estimate, In order to study parameterβestimation which base on the least squares and biased estimator especially the combining generalized Ridge and principal Components estimate. This paper discusses its superiority of the optimal and classical predictors based on the shrunken dimension biased estimate. In order to judge Multicellularity-Influential cases we raised two methods and examples of verification.This paper makes some research on the above mentioned question,the main result include the following.First, when the design matrix X ill-conditions We research some properties of The Combining Generalized Ridge and Principal Components Estimate ,Defined a relative efficiency .It was proved The Combining Generalized Ridge and Principal Components Estimate is better than least squares estimate under the MSE and GMSE principal, also better than Ridge estimate,Combining Ridge and Principal Components Estimate, Principal Components Estimate under the Pitman measure. It also proved the Combining Generalized Ridge and Principal Components Estimate is more efficiency than LS,Principal Components Estimate,The Combining Ridge and Principal ComponentsEstimate We proved the Combining Generalized Ridge and Principal Components Estimate was an admissible estimate.Secondly, Basing on the The Combining Generalized Ridge and Principal Components Estimation.We Consider the generalized linear regression model Y = Xβ+ε,ε-N(0,σ~2∑), A necessary and sufficient condition of comparison of its superiority of the optimal and classical predictors. An new method is proposed for the further research of superiority two predictors based on the shrunken dimension biased estimate.Thirdly , Basing on the Principal Components Estimate ,we discuss the Cook distance's perturbation analysis.We prove the equivalency of means-shift models and case-deletion models firstly.Deletion is employed and the exact deletion formula for Cook distance is gained,which not only simplifies the computation but also proposes a diagnostic for identifying influential observations.At last,we propose a principal component diagnose criterion for the multicollinearity- influential cases,whenη_i > 1.2,the cases are high multicollinearity-influential,so we have two methods for judging the multicollinearity-influential.