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Shrinkage reweighted regression

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  • Cabana Garceran del Vall, Elisa
  • Lillo Rodríguez, Rosa Elvira
  • Laniado Rodas, Henry

Abstract

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.

Suggested Citation

  • Cabana Garceran del Vall, Elisa & Lillo Rodríguez, Rosa Elvira & Laniado Rodas, Henry, 2019. "Shrinkage reweighted regression," DES - Working Papers. Statistics and Econometrics. WS 28500, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:28500
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    References listed on IDEAS

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    1. DeMiguel, Victor & Martin-Utrera, Alberto & Nogales, Francisco J., 2013. "Size matters: Optimal calibration of shrinkage estimators for portfolio selection," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3018-3034.
    2. Christophe Croux & Stefan Aelst & Catherine Dehon, 2003. "Bounded influence regression using high breakdown scatter matrices," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 265-285, June.
    3. Agulló, Jose & Croux, Christophe & Van Aelst, Stefan, 2008. "The multivariate least-trimmed squares estimator," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 311-338, March.
    4. Daniel Arribas-Bel & Jorge E Patino & Juan C Duque, 2017. "Remote sensing-based measurement of Living Environment Deprivation: Improving classical approaches with machine learning," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-25, May.
    5. Hawkins D. M. & Olive D. J., 2002. "Inconsistency of Resampling Algorithms for High-Breakdown Regression Estimators and a New Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 136-159, March.
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    Keywords

    Robust Regression;

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