  A robust estimator is proposed for the parameters that characterize the
linear regression problem. It is based on the notion of shrinkages, often used
in Finance and previously studied for outlier detection in multivariate data. A
thorough simulation study is conducted to investigate: the efficiency with
normal and heavy-tailed errors, the robustness under contamination, the
computational times, the affine equivariance and breakdown value of the
regression estimator. Two classical data-sets often used in the literature and
a real socio-economic data-set about the Living Environment Deprivation of
areas in Liverpool (UK), are studied. The results from the simulations and the
real data examples show the advantages of the proposed robust estimator in
regression.
