Proceedings of the 1st International Conference on Statistics and Analytics, ICSA 2019, 2-3 August 2019, Bogor, Indonesia

Research Article

Study of Robust Regression Modeling Using MM-Estimator and Least Median Squares

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  • @INPROCEEDINGS{10.4108/eai.2-8-2019.2290533,
        author={Khusnul  Khotimah and Kusman  Sadik and Akbar  Rizki},
        title={Study of Robust Regression Modeling Using MM-Estimator and Least Median Squares},
        proceedings={Proceedings of the 1st International Conference on Statistics and Analytics, ICSA 2019, 2-3 August 2019, Bogor, Indonesia},
        publisher={EAI},
        proceedings_a={ICSA},
        year={2020},
        month={1},
        keywords={least median squares multi-stage method outliers robust regression root mean squares error},
        doi={10.4108/eai.2-8-2019.2290533}
    }
    
  • Khusnul Khotimah
    Kusman Sadik
    Akbar Rizki
    Year: 2020
    Study of Robust Regression Modeling Using MM-Estimator and Least Median Squares
    ICSA
    EAI
    DOI: 10.4108/eai.2-8-2019.2290533
Khusnul Khotimah1,*, Kusman Sadik1, Akbar Rizki1
  • 1: Statistics, IPB University, Bogor, 16680,Indonesia
*Contact email: khusnulrfa@gmail.com

Abstract

Ordinary least squares (OLS) is a method commonly used to estimate regression equations. One solution handle OLS limitation to outlier problem is to use the robust regression method. This study used least-median squares (LMS) and multi-stage method (MM) robust regression. Simulation results of regression analysis in various scenarios are concluded that LMS and MM methods have better performance compared to OLS on data containing vertical and bad leverage point outliers. MM method has lowest average parameter estimation bias, followed by LMS, then OLS. LMS has smallest average root mean squares error (RMSE) and highest average R^2 is followed by MM then OLS. The results of the regression analysis comparison of the three methods on Indonesian rice production data in 2017 which contains 10% outliers were concluded that the LMS is the best method. The LMS produces the smallest RMSE of 4.44 and the highest R^2 that is 98%.