B0330
Title: A cellwise robust lasso estimator
Authors: Ines Wilms - Maastricht University (Netherlands) [presenting]
Lea Bottmer - Maastricht University (Netherlands)
Christophe Croux - Edhec Business School (France)
Abstract: The high-dimensional multiple regression model is an important workhorse for data scientists. The lasso is a popular estimator to reduce the dimensionality by imposing sparsity on the estimated regression parameters. The lasso is, however, not a robust estimator. Nevertheless, outliers frequently occur in high-dimensional datasets. We propose the sparse shooting $S$, a cellwise robust lasso estimator. The resulting regression coefficients are sparse, meaning that many of them are set to zero, hereby selecting the most relevant predictors. As such, the sparse shooting $S$ is computable in high-dimensional settings with more predictors than observations. Moreover, a distinct feature of this estimator is its ability to deal with cellwise contamination, where many cells of the design matrix of the predictor variables may be outlying. We compare its performance to several other sparse and/or robust regression estimators.
