Sparse partial robust M regression

•Sparse partial robust M regression is a dimension reduction and regression algorithm.•It is robust with respect to both vertical outliers and leverage points.•Intrinsic variable selection via sparse modeling can increase the model precision.•An implementation of the method is available in the software environment R.•We demonstrate the advantages of the method in a simulation study and for real data.

Sparse partial robust M regression is introduced as a new regression method. It is the first dimension reduction and regression algorithm that yields estimates with a partial least squares like interpretability that are sparse and robust with respect to both vertical outliers and leverage points. A simulation study underpins these claims. Real data examples illustrate the validity of the approach.