Robust Linear Regression Using L1-Penalized MM-Estimation for High Dimensional Data
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 3, May 2015, Pages: 78-84
Received: Mar. 10, 2015;
Accepted: Mar. 24, 2015;
Published: Mar. 30, 2015
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Kamal Darwish, Yildiz Technical University, Department of Statistics, Istanbul, Turkey
Ali Hakan Buyuklu, Yildiz Technical University, Department of Statistics, Istanbul, Turkey
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.
Ali Hakan Buyuklu,
Robust Linear Regression Using L1-Penalized MM-Estimation for High Dimensional Data, American Journal of Theoretical and Applied Statistics.
Vol. 4, No. 3,
2015, pp. 78-84.
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