Simultaneous Variable Selection And Semiparametric Estimation Of High Dimensional Logistic Models With Multiple Nonlinear Structure

As everyone knows, the Logistic model is a generalized linear regression analysis model. It has important applications in medicine, economics and other fields. This paper will introduce the high dimensional Logistic regression model with multivariate nonlinear structure. The model has high dimensional linear part and multiple nonlinear part. In this paper, we perform variable selection and parameter estimation of the linear part by using the method of Lasso combined with EBIC criterion. The processing of the nonlinear part is divided into two types:estimation and variable selection. This paper will use the theories of RKHS (reproducing kernel Hilbert space) and the methods based on the SS-ANOVA, then combined with GCV criterion to estimate the nonlinear part. We also used the Lasso method combined with EBIC criterion for variable selection of the nonlinear part. In the method, the realization process of linear and nonlinear parts all have tuning parameters. A large number of simulation results are also given in this paper, and then the feasibility and advantages of the algorithm are analyzed and compared. Finally, an example is used to demonstrate the practicability and superiority of the method used in this paper. The main work of this paper is:the introduction of the algorithm for the model, a large number of numerical simulation and empirical analysis of the algorithm.