Robust Estimation And Variable Selection Of Two Kinds Of Semi-parametric Models Under High Dimension Data

With the continuous progress of information technology,more and more data information and high-dimensional variable factors are involved in the field of semiparametric statistics.How to screen out the variable factors that have significant impacts on response variables is the research content of variable selection.This article mainly discusses robust estimation and variable selection of two kinds of semiparametric models based on modal regression under high-dimensional data.In the second chapter,we study the variable selection and robust estimation for partially variable coefficient model under high-dimensional data.Using B-spline basic function to approximate the unknown regression function in the model,and the loss function is established by combining modal regression with Bridge estimation method under high-dimensional.The nonzero important variables corresponding to parameter components and nonparametric components in the model are screened and their consistent estimations are given by applying appropriate regularization conditions,the Oracle properties of penalty estimation are obtained and proved.In the numerical simulation part,Bridge estimation is compared with LASSO and SCAD two estimation methods,and the analysis results reflected the superiority of Bridge estimation in variable selection.In the third chapter,we discuss the variable selection for partially linear additive model under high-dimensional data.Inspired by Bridge estimation,this paper constructs adaptive Bridge estimation by applying different weights to penalty function according to the importance of explanatory variables.In the framework of modal regression and adaptive Bridge estimation,the penalty objective function is constructed to realize the variable selection of high-dimensional sparse model.Based on the EM algorithm and the LQA algorithm,we get the algorithm suitable for this paper.The robust estimation of corresponding coefficient of the parametric and nonparametric part in the model are obtained by implement algorithm.In the part of theoretical proof and numerical simulations,the Oracle property of the adaptive Bridge estimation is verified.We illustrated the effectiveness and robustness of adaptive Bridge estimation by comparing with the LASSO penalty method.