SIMULATION STUDY OF ROBUST REGULATORS PARISETER AND SIDER-S ROBUST PARAMETERS IN LONGITUDINAL DATA WITH A VARIETY OF LEVELS
DOI:
https://doi.org/10.61841/tewyfp95Keywords:
Longitudinal Data, Robust Regression, Outliers, M-Estimator, S-EstimatorAbstract
Robust regression is used to obtain the right model when the data contains outliers and are not normally distributed. Robust regression has several kinds of estimators, one of which is using M-estimator and S-estimator. The M-estimator robust regression is the simplest approach both computationally and theoretically while the S-estimator is an estimator that has a high breakdown point for estimating error scales. This study wants to find out the comparison of M-estimator and S-estimator robust estimation regression that is more efficient by comparing the variance between estimators using relative efficiency in longitudinal simulation data. The results showed that the model with parameter estimators obtained from the S-estimator robust regression method was more effectively used to predict malnutrition in East Java Regency / City in 2013 - 2018 compared to the M-estimator robust regression method.
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References
[1] BPS Jatim. 2018. Badan Pusat Statistik Jawa Timur. Diakses di http://www. bpsjatim. com/ (diakses 1 Oktober 2019).
[2] Cousineau, D. dan Chartier, S. 2010. Outlier detection and treatment. International Journal of Psychological Research, 3(1), 58–67.
[3] Danardono. 2018. Analisis Data Longitudinal. Yogyakarta: Gadjah Mada University Press
[4] Drapper, N. dan H. Smith. 1992. Analisis Regresi Terapan (Edisi Kedua). Jakarta: Gramedia Pustaka Utama.
[5] Fernandes, A.A.R.,Nyoman Budiantara, I.,Otok, B.W.,Suhartono, (2014), “Spline estimator for bi-responses nonparametric regression model for longitudinal data ”, Applied Mathematical Sciences, Vol 8 No 114, pp 5653-5665.
[6] Fernandes, A.A.R.,Nyoman Budiantara, I.,Otok, B.W.,Suhartono, (2014), “Reproducing Kernel Hilbert space for penalized regression multi-predictors: Case in longitudinal data”, International Journal of Mathematical Analysis, Vol 8 No 40, pp 1951-1961.
[7] Fernandes, A.A.R, Budiantara, I.N, Otok, B.W., and Suhartono. (2015). “Spline Estimator for Bi-Responses and Multi-Predictors Nonparametric Regression Model in Case of Longitudinal Data”, Journal of Mathematics and Statistics, Vol 11, No 2, pp. 61-69.
[8] Fernandes, A.A.R, Jansen, P., Sa’adah, U, Solimun, Nurdjannah, Amaliana, L., and Efendi, A. (2018). “Comparison of Spline Estimator at Various Levels of Autocorrelation in Smoothing Spline Nonparametric Regression For Longitudinal Data”, Communications in Statistics – Theory and Methods, Vol 46, No 24, pp 12401-12424.
[9] Fernandes, A.A.R., Hutahayan, B., Solimun, Arisoesilaningsih, E., Yanti, I., Astuti, A.B., Nurjannah, & Amaliana, L, (2019), “Comparison of Curve Estimation of the Smoothing Spline Nonparametric Function Path Based on PLS and PWLS In Various Levels of Heteroscedasticity”, IOP Conference Series: Materials Science and Engineering, Forthcoming Issue.
[10] Huber, P. J. (1973). Robust regression: asymptotics, conjectures and Monte Carlo. The Annals of Statistics, 1(5), 799-821.
[11] Hutahayan, B., Solimun, Fernandes, A.A.R., Arisoesilaningsih, E., Yanti, I., Astuti, A.B., Nurjannah, & Amaliana, L, (2019), “Mixed Second Order Indicator Model: The First Order Using Principal Component Analysis and The Second Order Using Factor Analysis”, IOP Conference Series: Materials Science and Engineering, Forthcoming Issue.
[12] Kutner, M. H., Nachtsheim, C. J., Neter, J. dan Li, W. 2004. Applied Linier Regression Models. Fifth Edition. McGraw-Hill Companies, Inc. New York.
[13] Lainun, H., Tinungki, G. M., & Amran, A. (2018). Perbandingan Penduga M, S, dan MM pada Regresi Linier dalam Menangani Keberadaan Outlier. Jurnal Matematika, Statistika dan Komputasi, 15(1), 88-96.
[14] Mentari, H. W. 2019. Pendugaan Parameter Analisis Regresi Robust Penduga-M dan Penduga-S Pada Data Simulasi dengan Berbagai Tingkat Pencilan. Skripsi: Universitas Brawijaya.
[15] Rousseeuw, P. and Yohai, V. 1984. Robust regression by means of S-estimators. In Robust and nonlinear time series analysis (pp. 256-272). Springer. New York, NY.
[16] Susanti, Y., Pratiwi, H., Sulistijowati, H., and Liana, T. 2014. M Estimation, S Estimation, and MM Estimation In Robust Regression. International Journal of Pure and Applied Mathematics. 91(3), 349-360.
[17] Wackerly, D., et al. 2008. Mathematical Statistics with Applications 7th issue. Thomson Brooks/Cole. Florida.
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