  We propose a robust variable selection procedure using a divergence based
M-estimator combined with a penalty function. It produces robust estimates of
the regression parameters and simultaneously selects the important explanatory
variables. An efficient algorithm based on the quadratic approximation of the
estimating equation is constructed. The asymptotic distribution and the
influence function of the regression coefficients are derived. The widely used
model selection procedures based on the Mallows's $C_p$ statistic and Akaike
information criterion (AIC) often show very poor performance in the presence of
heavy-tailed error or outliers. For this purpose, we introduce robust versions
of these information criteria based on our proposed method. The simulation
studies show that the robust variable selection technique outperforms the
classical likelihood-based techniques in the presence of outliers. The
performance of the proposed method is also explored through the real data
analysis.
