Robust variable section with the sparse shooting S

In multiple regression analysis, a response variable is predicted based on a set of many predictor variables. We are particularly interested in high-dimensional multiple regression analysis where a large number of predictors is available. The lasso has become a popular estimator to reduce the dimensionality of such high-dimensional regression models by imposing sparsity on the estimated regression parameters. As such, the lasso performs variable selection since it only keeps a few predictors and discards the remaining predictors by setting their respective parameter estimates to zero. The lasso is, however, not a robust estimator. Nevertheless, outliers, i.e. atypical observations, frequently occur in high-dimensional data sets. Therefore, we propose a cellwise robust lasso estimator, the sparse shooting S. This estimator can deal with cellwise contamination, where many cells of the design matrix of the predictor variables may be outlying. Moreover, the sparse shooting S is computable in high-dimensional settings with more predictors than observations and it gives sparse parameter estimates. We compare its performance to several other sparse and/or robust regression estimators.status: publishe