COMPARATIVE STUDY OF SOME ESTIMATORS OF LINEAR REGRESSION MODELS IN THE PRESENCE OF OUTLIERS

  • A. Ibrahim
  • I. J. Dike
  • A. B. Badawaire
Keywords: Estimation, Estimator, Outliers, Performance, Regression, Robust

Abstract

The paper examined the performance of five estimation methods using six different outlier percentages (0%, 5%, 10%, 20%, 30% and 40%) and five different sample sizes (20, 40, 60, 100 and 200) were used to investigate effect of sample size on the performance of each of the estimation methods. The study adopted absolute bias, variances, relative efficiency and root mean square errors as comparison criteria through Monte-Carlo experiment and real life data was used to validate the simulation results. The study found that, under 5%, 10%, 20% and 30% outlying condition Robust-MM is the most preferred estimator across all criteria and sample size except using relative efficiency criterion and when the sample size is 40, 200 and 200 under 5%, 20% and 30% outlying condition and using absolute bias criterion respectively while Robust-LTS is the least preferred estimator except when the sample size is 40, 20 ; 40, 20 ; 20, 200 under 5%, 20% and 30% outliers and using absolute bias, variance and root mean square error respectively. Under 40% outlying condition Robust-MM is the most preferred estimator across all criteria and sample size except using relative efficiency and when the sample size is 20. Furthermore, Robust-MM is the most consistent estimator across the comparison criteria except when using relative efficiency and sample size has little or no effect on the performance of the estimators across all the different outlier levels. R Statistical package was used for the data analysis. This study therefore recommends the used of Robust-MM estimator

References

REFERENCES

Alma, O. G. (2011). Comparison of robust regression methods in linear regression. International Journal for contempMaths and Science, 6: 409-421.

DasGupta, M. & Mishra, S.K. (2004). Least absolute deviation estimation of linear econometric models: A literature review. Available:http://mpra.ub.uni muenchen.de/7 81.

David D. (2014). Comparison of Robust Regression Estimators. M.phil thesis, Kwameh Nkurumah University of Science and technology, Ghana, Ghana.

Hampel, F. (2001). Robust statistics: A brief introduction and overview. Pages 1-5. In David D. (2014). Comparison of Robust Regression Estimators

Huber, P. J. (1972). The 1972 wald lecture: Robust statistics. The Annals of Mathematical Statistics, 43: 1041-1067. In David D. (2014). Comparison of Robust Regression Estimator.

Hawkins, D. (1980). Identification of Outliers. Chapman and Hall. London. In Edgar, A. & Caroline, R. (2004). On detection of outliers and their effect in supervised classification. Conference paper.

Liu H., Shah S. and Jiang W. (2004). On-line outlier detection and data cleaning. Computers and Chemical Engineering. In Maimon O. and Rockach L. (Eds.) (2005). Data Mining and Knowledge Discovery Handbook: A Complete Guide for Practitioners and Researchers.

Rousseeuw, P. J. (1984). Robust Regression and Outlier Detection.JOHN WILEY and SONS.

Rousseeuw, P. J. &Yohai, V. J. (1984). Robust Regression by Mean of S Estimators. Robust and Nonlinear Time Series Analysis, 256-274, doi: 10.1007/978-1-4615-7821-5-15.

Stephen, R. &Senthamarai, K. K. (2017). Detection of Outliers in Regression Model for Medical Data. International Journal of Medical Research &Health Sciences, 6(7), 50-56.

Williams, G. J., Baxter, R. A., He H. X. & Hawkins S., Gu L. (2002). A Comparative Study of RNN for Outlier Detection in Data Mining. IEEE International Conference on Data-mining. In: Maimon O. andRockach L. (Eds.) (2005). Data Mining and Knowledge Discovery Handbook: A Complete Guide for Practitioners and Researchers.

Yohai, V. J. (1987). High Breakdown Point and High Efficiency Robust Estimates for Regression. The Annals of Statistics, 15(20), 642-656, doi:10.1214/aos/1176350366.

Zimek, A. &Filzsomer, P. (2018). “There and Back again: Outlier detection between statistical reasoning and data mining algorithmâ€. Wiley Interdisciplinary Reviews: Data mining and Knowledge Discovery, 8(6). Doi:10.1002/widm.1280

Published
2022-04-12
How to Cite
IbrahimA., DikeI. J., & BadawaireA. B. (2022). COMPARATIVE STUDY OF SOME ESTIMATORS OF LINEAR REGRESSION MODELS IN THE PRESENCE OF OUTLIERS. FUDMA JOURNAL OF SCIENCES, 6(1), 368 - 376. https://doi.org/10.33003/fjs-2022-0601-908