Exact Selective Inference Based On Several Penalty Methods

Post-selection inference has been an active research topic recently.Data leading model has become a new development boom.Many scholars have provided different approaches to solve practical problems in many fields such as medicine and finance and so on.The main results focus on selective inference under linear models.In this dissertation,it is firstly extended to generalized linear models and selective inference based on penalized least square method is proposed.The core of the framework is based on the conditional distribution function of selection events,and the effective confidence interval of the selected coefficients is constructed according to the sampling distribution theorem by using Lasso and the elastic network selection model.A large number of numerical simulation experiments were carried out,and the proposed method was applied to the diabetes data set and the Breast cancer Wisconsin diagnostic data.With the continuous progress of information technology,data becomes more complex and changeable.When modeling high-dimensional data in real life,it is found that the linear assumption and the generalized linear assumption are sometimes too strict to be applicable.On this basis,this dissertation further extends the method to semi-parameter single index model and partial linear model,enlarges the practical application range,and proposes a selective inference method for single index model and partial linear model.In this dissertation,the unknown smooth function is estimated by the local polynomial expansion method,and then the model is selected based on the Lasso penalized least square method.Then the selective inference is made by the exact sampling distribution theorem,and the numerical simulation is given,which shows that the method has good competitiveness.