상관성이 높은 공변량 자료에서 그룹변수 선택 방법을 위한 벌점화 방법 연구

학위논문 (박사)-- 서울대학교 대학원 : 통계학과, 2013. 2. 김용대.This paper considers a problem of model selection and estimation in sparse, high-dimensional regression models where covariates are grouped. We propose a new regularization method which can reflect a correlation structure between groups. We propose a combination of group MCP penalty and groupwise quadratic penalty called groupwise weighted ridge penalty. The former ensures groupwise sparsity and the later promotes simultaneous selection of highly correlated groups. We show that this estimator satisfes the group selection consistency. We drive the optimization algorithm for the proposed method. Numerical studies show that this estimator appears to perform well in comparisons with other existing methods.1 Introduction 1.1 Overview 1.2 Outline of the thesis 2 Literature review : Variable selection 2.1 Individual variable selection 2.2 Group variable selection 3 New penalized method 3.1 Sparse groupwise weighted ridge penalty 3.2 Theoretical properties 4 Computation 4.1 Group Lasso 4.1.1 Orthogonal case 4.1.2 General case 4.2 Group Laplacian method 4.2.1 Orthogonal case 4.2.2 General case 4.3 Convex concave procedure 4.4 Sparse groupwise weighted ridge 4.4.1 Orthogonal case 4.4.2 General case 5 Numerical studies 5.1 Simulation studies 5.2 Real data 5.2.1 Wine quality 5.2.2 Microarray gene expression data 6 Concluding remarks Abstract (in Korean)Docto