The growing need for dealing with big data has made it necessary to find computationally efficient methods for identifying important factors to be considered in statistical modeling. In the linear model, the LASSO is an effective way of selecting variables using penalized regression. It has spawned substantial research in the area of variable selection for models that depend on a linear combination of predictors. However, with the exception of a few instances, there are has not been much work addressing the lack of optimality of variable selection when the model errors are not Gaussian and/or when the data contain gross outliers. We propose the signed-rank LASSO as a robust and efficient alternative to LAD and LS LASSO. As LAD LASSO, the approach is appealing for use with big data since one can use data augmentation to perform the estimation as a single weighted L1 optimization problem.
This is based on joint work with Huybrechts F. Bindele.