Robust Variable Selection Based On Adaptive Group Bridge

Variable selection plays a vital role in dealing with the data.An efficient variable selec-tion method can yield a simple model by removing the redundant covariates.Furthermore,a good method of variable selection can produce a better prediction accuracy.In addition,the variable selection method based on the penalization has always been one of the hot issues studied by statisticians for over 20 years.Compared with the traditional approaches,the penalized methods have an unparalleled advantage in studying the data.The reason is that the penalized methods can simultaneously complete variable selection and parameter esti-mation.In application,covariates possess a grouping structure that can be incorporated into the analysis,and there are usually outliers in covariates and response variable.Therefore,it is important to find a way to deal with outliers and select important groups as well as important members of those groups.This dissertation contains four chapters.Chapter one gives an overview of the research on the method of estimation and group selection.Chapter two is the main content of the paper,including the introduction of our method and thcorctical properties.We propose a adjusted WLAD regression estimation,which combines the excellent properties of WLAD and least squares estimation to achieve a robust estimation and applies adaptive group bridge method to select variables not only at group level but also at within-group level.In addition,we give the theoretical properties of the proposed method,including the consistency of the estimators,variable selection consistency and the asymptotic normality of estimators.Furthermore,the proofs of theoretical results arc given under appropriate conditions.In the chapter three,we conduct numerical simulations based on three cases data from the lincar model,and obtain good numerical results.In application,this paper analyzes Boston housing data and ?-carotene level data to illustrate the performance of our method when there are both outliers in both covariates and the response variable.The results show that our method performs better than group bridge.Chapter four is the summary of this paper.