Robust variable selection for nonlinear models with diverging number of parameters

•A robust variable selection for nonlinear models is proposed.•We establish the theoretical properties of our procedure.•A modified MEM algorithm for the proposed estimation procedure is proposed.

We focus on the problem of simultaneous variable selection and estimation for nonlinear models based on modal regression (MR), when the number of coefficients diverges with sample size. With appropriate selection of the tuning parameters, the resulting estimator is shown to be consistent and to enjoy the oracle properties.