| With the continuous development of modern science and technology and the continuous improvement of data collection technology,researchers can collect a lot of high-dimensional data from various fields.At present,variable selection under high-dimensional data has been developed.But most of these studies only consider the selection of variables for main effects.However,in practice,the main effects alone may not be enough to describe the relationship between response and the prediction.Therefore,the variable selection problem with interac-tion terms under high-dimensional data is more meaningful.Based on this,this paper mainly discusses the two-stage regularization method of semiparametric models with interaction terms under high-dimensional data and the variable selection problem under the marginal principle.In chapter 2,based on the semiparametric model with interaction terms,a two-stage regularization method based on B-spline basis function approximation and double adaptive LASSO penalty function is proposed.In stage 1,the B-spline basis function is used to approximate the non-parameter function,and the simultaneous variable selection of parametric and non-parametric components is realized based on mode regression and adaptive LASSO estimation.To maintain the hierarchy,in stage 2,only the variable selection of the interaction item is carried out,the important interaction effect is obtained,and the nature of the Oracle of the selected variable and the consistency of the hierarchy are proved,and the spe-cific calculation algorithm and adjustment parameter selection details are given.The nu-merical simulation further verifies the excellent properties of the proposed method.In chapter 3,considering the variable selection characteristics of the two-stage regularization method,the whole solution path is highly dependent on the variable selection results of the first stage.Based on this,this chapter considers the regularization method based on the marginal principle,so that main terms and interaction terms can be selected at the same time.Firstly,CDAR based on the coordinate descent algorithm and combined with genetic conditions.Secondly,the screening consistency of the CDAR algorithm is proved.Finally,numerical simulation verifies the superiority of the algorithm. |
