Robust regression based on shrinkage with application to Living Environment Deprivation Articles uri icon

publication date

  • February 2020

start page

  • 293

end page

  • 310


  • 2


  • 34

International Standard Serial Number (ISSN)

  • 1436-3240

Electronic International Standard Serial Number (EISSN)

  • 1436-3259


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


  • robust regression robust mahalanobis distance shrinkage estimator outliers environmental study