Variable Selection Of Generalized Linear Models And Partially Variable Coefficient Models With Interaction Terms Under High-dimensional Data

With the development of science and technology,variable selection plays an important role with the dimensionality of the data getting higher and higher.An effective variable selection method can improve the accuracy and interpretability of model prediction by screening out unimportant variables and obtaining a concise model.In recent years,applying penalty methods for variable selection has attract-ed a lot of attention from statisticians.The penalty method can not only work out parameter estimates while selecting variables,but also reduce the amount of calculation.Therefore,compared with traditional variable selection methods,the variable selection method of penalty estimation has high advantages.This article mainly discusses the asymptotic properties and variable selection of generalized linear models and partial variable coefficient models with interaction terms in the case of high-dimensional data.In chapter 2,the objective function of penalty estimation is constructed by using logarithmic likelihood function and adaptive bridge penalty estimation and the problem of parameter estimation and variable selection for generalized linear models with high dimensional data is stud-ied.Under appropriate regular conditions,the consistency and Oracle properties of the adaptive bridge estimator are proved,and the finite sample properties of the proposed method are verified by numerical simulation and case analysis.In chapter 3,the chapter focus on the variable selection for interactive partial variable coef-ficient models under high dimensional data.In order to simplify the model,we only explore interaction effects of linear part where the model must maintain the heredity structure between main effects of linear parts and interaction effects.In the two-stage variable selection,the non-parametric function is approximated by B-spline basic function,penalty objective function is constructed by SCAD penalty function.To work out penalty estimate for linear parts,interaction parts and non-parametric parts,we don't consider interactive effects in the first stage.The model in the second stage consists of the variables selected in the first stage and interac-tion effects.Then,under proper regularization conditions,the consistency,Oracle properties and the consistency of the hierarchical structure are proved.Numerical simulations verified the performance of the proposed methods in a finite sample.