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Abstract

Outliers in a statistical analysis strongly affect the performance of the ordinary least squares, such outliers need to be detected and extreme outliers  deleted. Thisp is aimed at proposing a Redescending M-estimator which is more efficient and robust compared to other existing methods. The results show that the proposed method is effective in detection and deletion of extreme outliers compared to the other existing ones.

Keywords

Efficiency M-estimator Redescending M-estimator OUtliers Robustness

Article Details

How to Cite
Anekwe, S., & Onyeagu, S. (2021). The Redescending M estimator For detection and deletion of Outliers in Regression analysis. Pakistan Journal of Statistics and Operation Research, 17(4), 997-1014. https://doi.org/10.18187/pjsor.v17i4.3546

References

    References
    Aggarwal, C. & Yu, P. (2001), Outlier Detection for High Dimensional Data. In Proceedings of the ACM SIGMOD International Conference on Management of Data. ACM Press, 37-46.
    Alamgir, A. A., Khan, S.A, Khan, D.M. & Khalil, U. (2013), A New Efficient Redescending M-estimator, Alamgir Redesending M-estimator. Research Journal of Recent Sciences, 2(8). 79 - 91.
    Andrew, D.F., Bickel, F.R. Hampel, P.J. Huber, Tukey J.W. & Rogers W.H. (1972), Robust Estimates of Location Survey and Advances, Princeton University Press, Princeton, NJ.
    Atkinson, A. (1994), Fast Very Robust Methods for the Detection of Multiple Outliers, Journal of American Statistical Association, 89, 1329-1339.
    Beaton, A.E. & Tukey, J.W. (1974), The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data. Tecnometrics, 16, (2), 147-185.
    Becker, C. & Gather, U. (1999), The Masking Breakdown Point of Multivariate Outlier Identification Rule, Journal of the American Statistical Association, 94, 949-955.
    Carling, K. (2000), Resistant Outlier Rules and Non-Gaussian Case, Computational Statistics and Analysis, Vol. 33, 249 – 258.
    Draper, N.R. & Smith H. (1998), Applied Regression Analysis, Third Edition, John Wiley and Sons, New York.
    Hadi, A.S. & Simonoff J.S. (1993), Procedures for Identification of Multiple Outliers in Linear Models, Journal of the American Statistical Association, 88(424), 1264- 1272.
    Hampel, F.R. (1974), The Influence Curve and Its Role in Robust Estimation, Journal of the American Statistical Association, Vol. 69, No 346, pp. 383-393.
    Hampel, F.R. (1997), Some Additional Notes on the ‘Princeton Robustness Year,’ In: The Practice of Data Analysis: Essays in Honour of Tukey J.W. eds Brillinger, D.R., and Ferholz, L.T. Princeton: Princeton University press, 133-153.
    Hampel, F.R., Ronchetti, E.M. Rousseeuw, P.J. & Stahel, W.A. (1986), Robust Statistics. The Approach Based on Influence Functions. New York: John Wiley.
    Hawkins, D.M., Bradu, D. & Kass, G. V. (1984), Location of several outliers in multiple regression data using elemental sets. Technometrics 26, 197-208.
    Huber, P.J. (1964), Robust Estimation of Location Parameter. The Annals of Mathematical Statistics, 35, 73 – 101.
    Nguyena T.D. & Welch, R. (2010), Outlier Detection and Least Trimmed Squares Approximation using Semi-definite Programming, Comput Stat Data, 54: 3212-3226.
    Rousseeuw, P.J. (1982), Least Median of Squares Regression, Research Report No. 178, Centre for Statistics and Operations Research, VUB Brussels.
    Rousseeuw, P.J. (1983), Multivariate Estimation with High Breakdown point, Research Report No. 192, Centre for Statistics and Operations Research, VUB Brussels.
    Rousseeuw, P.J. & Leroy, A.M. (1987), Robust Regression and Outlier Detection, Wiley-Interscience, New York.
    Rousseeuw, P.J. & Yohai, V. (1984), “Robust Regression by Means of S-Estimators”, in Robust and Nonlinear Time Series, edited by J. Franke, W. Hardle, and R.D. Martin, Lecture Notes in Statistics 26, Springer Verlag, New York, 256-274.
    Sokal, R.R & Rohlf, F. J. (2012), Biometry, 4th Edition. W.H. Freeman and Co, New York.
    Tukey, J. W. (1977), Exploratory Data Analysis. Reading, MA: Addison–Wesley.
    Zhang, L., Li, P., Mao, J., Ma, F., Ding, X. & Zhang, Q. (2015), An Enhanced Monte Carlo Outlier Detection Method, J Comput Chem. (2015) 36(25), 1902-6. DOI: 10.1002/jcc.24026. Epub 2015 Jul 31.