  Several regularization methods have been considered over the last decade for
sparse high-dimensional linear regression models, but the most common ones use
the least square (quadratic) or likelihood loss and hence are not robust
against data contamination. Some authors have overcome the problem of
non-robustness by considering suitable loss function based on divergence
measures (e.g., density power divergence, gamma-divergence, etc.) instead of
the quadratic loss. In this paper we shall consider a loss function based on
the R\'enyi's pseudodistance jointly with non-concave penalties in order to
simultaneously perform variable selection and get robust estimators of the
parameters in a high-dimensional linear regression model of non-polynomial
dimensionality. The desired oracle properties of our proposed method are
derived theoretically and its usefulness is illustustrated numerically through
simulations and real data examples.
