  Cellwise outliers are widespread in data and traditional robust methods may
fail when applied to datasets under such contamination. We propose a variable
selection procedure, that uses a pairwise robust estimator to obtain an initial
empirical covariance matrix among the response and potentially many predictors.
Then we replace the primary design matrix and the response vector with their
robust counterparts based on the estimated covariance matrix. Finally, we adopt
the adaptive Lasso to obtain variable selection results. The proposed approach
is robust to cellwise outliers in regular and high dimensional settings and
empirical results show good performance in comparison with recently proposed
alternative robust approaches, particularly in the challenging setting when
contamination rates are high but the magnitude of outliers is moderate. Real
data applications demonstrate the practical utility of the proposed method.
