Robust and sparse multinomial regression in high dimensions

A robust and sparse estimator for multinomial regression is proposed for high dimensional data. Robustness of the estimator is achieved by trimming the observations, and sparsity of the estimator is obtained by the elastic net penalty. In contrast to multi-group classifiers based on dimension reduction, this model is very appealing in terms of interpretation, since one obtains estimated coefficients individually for every group, and also the sparsity of the coefficients is group specific. Simulation studies are conducted to show the performance in comparison to the non-robust version of the multinomial regression estimator, and some real data examples underline the usefulness of this robust estimator particularly in terms of result interpretation and model diagnostics.