Robust Linear Regression Using L1 Penalized MM Estimation for High Dimensional Data
American Journal of Theoretical and Applied Statistics, 2016 (Peer-Reviewed Journal)
- Publication Type: Article / Article
- Publication Date: 2016
- Doi Number: 10.11648/j.ajtas.20150403.12
- Journal Name: American Journal of Theoretical and Applied Statistics
- Open Archive Collection: AVESIS Open Access Collection
- Yıldız Technical University Affiliated: Yes
Abstract
Large datasets, where the number of predictors p is larger than the sample sizes n, have become very popular in recent years. These datasets pose great challenges for building a linear good prediction model. In addition, when dataset contains a fraction of outliers and other contaminations, linear regression becomes a difficult problem. Therefore, we need methods that are sparse and robust at the same time. In this paper, we implemented the approach of MM estimation and proposed L1-Penalized MM-estimation (MM-Lasso). Our proposed estimator combining sparse LTS sparse estimator to penalized M-estimators to get sparse model estimation with high breakdown value and good prediction. We implemented MM-Lasso by using C programming language. Simulation study demonstrates the favorable prediction performance of MM-Lasso.