Regularized least weighted squares estimator in linear regression

Abstrakt

This article is interested in estimating parameters of the linear regression model in a high-dimensional setting, i.e. with a large number of regressors. The lasso estimator does not possess high robustness with respect to the presence of outliers in the data. Our approach extends the least weighted squares estimator, which has appealing robustness and efficiency properties in linear regression with a small number of regressors. The novel LWS-lasso estimator is proposed here as an L1-regularized version of the least weighted squares. The analysis of a world tourism dataset as well as simulations show that LWS-lasso may outperform available regression estimators, especially in scenarios with high-dimensional data with a higher contamination by outliers.