Groupwisely Sparse Penalty for Highly Correlated Covariates
상관성이 높은 공변량 자료에서 그룹변수 선택 방법을 위한 벌점화 방법 연구
- 자연과학대학 통계학과
- Issue Date
- 서울대학교 대학원
- Group variable selection; high-dimensional data; penalized regression; weighted ridge; oracle property.
- 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.