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Robust Three-Step Regression Based on Comedian and Its Performance in Cell-Wise and Case-Wise Outliers

Author

Listed:
  • Henry Velasco

    (Department of Mathematical Sciences, Universidad Eafit, Medellín 050022, Colombia)

  • Henry Laniado

    (Department of Mathematical Sciences, Universidad Eafit, Medellín 050022, Colombia)

  • Mauricio Toro

    (Department of Informatics and Systems Engineering, Universidad Eafit, Medellín 050022, Colombia)

  • Víctor Leiva

    (School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile)

  • Yuhlong Lio

    (Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA)

Abstract

Both cell-wise and case-wise outliers may appear in a real data set at the same time. Few methods have been developed in order to deal with both types of outliers when formulating a regression model. In this work, a robust estimator is proposed based on a three-step method named 3S-regression, which uses the comedian as a highly robust scatter estimate. An intensive simulation study is conducted in order to evaluate the performance of the proposed comedian 3S-regression estimator in the presence of cell-wise and case-wise outliers. In addition, a comparison of this estimator with recently developed robust methods is carried out. The proposed method is also extended to the model with continuous and dummy covariates. Finally, a real data set is analyzed for illustration in order to show potential applications.

Suggested Citation

  • Henry Velasco & Henry Laniado & Mauricio Toro & Víctor Leiva & Yuhlong Lio, 2020. "Robust Three-Step Regression Based on Comedian and Its Performance in Cell-Wise and Case-Wise Outliers," Mathematics, MDPI, vol. 8(8), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1259-:d:393167
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    References listed on IDEAS

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    2. Claudio Agostinelli & Andy Leung & Victor Yohai & Ruben Zamar, 2015. "Rejoinder on: Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 484-488, September.
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    Cited by:

    1. Ramón Giraldo & Luis Herrera & Víctor Leiva, 2020. "Cokriging Prediction Using as Secondary Variable a Functional Random Field with Application in Environmental Pollution," Mathematics, MDPI, vol. 8(8), pages 1-13, August.

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