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On the outlier Detection in Nonlinear Regression

Authors: Hossein Riazoshams, Midi Habshah, Jr., Mohamad Bakri Adam


The detection of outliers is very essential because of their responsibility for producing huge interpretative problem in linear as well as in nonlinear regression analysis. Much work has been accomplished on the identification of outlier in linear regression, but not in nonlinear regression. In this article we propose several outlier detection techniques for nonlinear regression. The main idea is to use the linear approximation of a nonlinear model and consider the gradient as the design matrix. Subsequently, the detection techniques are formulated. Six detection measures are developed that combined with three estimation techniques such as the Least-Squares, M and MM-estimators. The study shows that among the six measures, only the studentized residual and Cook Distance which combined with the MM estimator, consistently capable of identifying the correct outliers.

Keywords: Nonlinear Regression, outliers, Gradient, LeastSquare, M-estimate, MM-estimate.

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[1] Anskombe, F. J. and Tukey, J. w. (1963), The examination and analysis of residuals. Technometrics, 5, 141-60.
[2] Atkinson, A.C., (1981), Two graphical displays for outlying and influential observations in regression, Biometrika, 68, 1, 13-20.
[3] Atkinson, A.C., (1982), Regression Diagnostics, Transformations and Constructed Variables, Journal od Royal Statistical Society, B, 44, 1, 1- 36.
[4] Atkinson, A.C., (1986). Masking unmasked, Biometrika, 73, 3, 533-541.
[5] Bates, D.M. Watts, D.G., (1980). Relative curvature measures of nonlinearity, J. R. statist. Ser. B 42, 1-25.
[6] Belsley, D. A., Kuh, E., and Welsch, R. E. (1980), Regression Diagnostics, John Wiley & Sons, New York.
[7] Cook, R. D., and Weisberg, S., (1982), Residuals and Influence in Regression. CHAPMAN and HALL.
[8] Fox, T., Hinkley, D. and Larntz, K., (1980), Jackknifing in nonlinear regression. Technometrics, 22, 29-33.
[9] Habshah, M., Noraznan, M. R., Imon, A. H. M. R. (2009). The performance of diagnostic-robust generalized potential for the identification of multiple high leverage points in linear regression, Journal of Applied Statistics, 36(5):507-520.
[10] Hadi, A.H. (1992). A new measure of overall potential influence in linear regression, Computational Statistics and Data Analysis 14 (1992) 1-27.
[11] Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J. and Stahel, W.A. (1986), Robust Statistics: The Approach Based on InfluenceFunctions. New York: John Wiley & Sons, Inc.
[12] Hoaglin, D. C., Mosteller, F., Tukey, J. W. (1983), Understanding Robust and Exploratory Data Analysis, John Wiley and Sons.
[13] Hoaglin, D.C., & Wellsch, R. (1978). The hat Matrix in regression and ANOVA. Ammerican Statistician 32, 17-22.
[14] Huber, P. J. (1981), Robust Statistics, Wiley, New York .
[15] Imon, A.H.M.R, (2002), Identifying multiple high leverage points in linear regression, J. Stat. Stud. 3, 207-218.
[16] Kennedy. W. and Gentle, J. (1980). Statistical Computing. New York:Dekker.
[17] Rousseeuw, P. J., and Leroy, A. M. (1987), Robust Regression and outlier detection, New York: John Wiley.
[18] Riazoshams, H., Habshah, Midi, (2009), A Nonlinear regression model for chickens- growth data. European Journal of Scientific Research, 35, 3, 393-404.
[19] Srikantan, K. S. (1961), Testing for a single outlier in a regression model. Sankhya A, 23, 251-260.
[20] Stromberg, A. J., (1993), Computation of High Breakdown Nonlinear Regression Parameters, Journal of American Statistical Association, 88 (421), 237-244.
[21] Seber, G., A. F. and Wild, C. J. (2003), Nonlinear Regression, John Wiley and Sons.
[22] Yohai, V. J. (1987), High Breakdown point and high efficiency robust estimates for regression, The Annals of Statistics, 15, 642-656.