Variable Selection For Several Regression Models Via Elastic Net Procedure

With the popularity of the Internet and the rapid development of data collection technology, high-dimensional data has become a major challenge to the academic statistical data analysis. The variable selection method is a very effective high-dimensional data processing method, which can reduce the dimension and simplify the model. The Elastic Net procedure is a new variable selection method for data structure which strongly related variables. It can select variables effectively and estimate parameters. In this paper, we summarize and analyze the relevant research of the Elastic Net procedure. Then we study the characterization and applications of the Elastic Net procedure in several statistical models. The main research and results are as follows:The partially linear model is widely used more than the general linear model, so we put forward the Elastic Net procedure for the partial linear model. We focus on the group effect, i.e., strongly correlated predictors tend to be selected in groups. In addition, a numerical simulation is made to check the nature. Finally, we carry on the instance analysis to test that the Elastic Net procedure is particularly useful in high dimension, low sample size data.Poisson logarithm linearity model is a typical count variable model. In this paper we propose the Adaptive Elastic Net procedure for Poisson logarithm linearity model and prove the group effect of its estimation. Moreover, we obtain that the Adaptive Elastic Net procedure estimator for the parametric component of Poisson logarithm linearity model has the Oracle properties under some appropriate conditions. A numerical simulation is used to demonstrate the conclusion.Logistic regression model is a commonly model for dichotomous variables. We focus on variable selection and parametric estimation for Logistic regression model via the Adaptive Elastic Net procedure in this paper. We prove that the Adaptive Elastic Net procedure for the Logistic regression model has Oracle properties and group effect. In addition, we make a numerical simulation to demonstrate the conclusion.