Sains Malaysiana 29:103-118 (2000)                                                                            Pengajian Kuantitatif /

                                                                                                Quantitative Studies

 

Heteroscedastic Nonlinear Regression by

Using Tanh Psi Function

 

Habshah Midi

Jabatan Matematik

Universiti Putra Malaysia

43400 UPM Serdang, Selangor D.E.Malaysia

 

 

ABSTRACT

 

This article is concerned with the extension of heteroscedastic nonlinear regression estimation by using Tanh Psi function. The robustness properties of the Tanh's and Hampel's Weighted MM (WMM) estimators were investi­gated. In our simulation study, it has been shown that the biases and RMSE'S of the Hampel's estimates increase appreciably higher than the Tanh's estimates as the percentage of outliers increases. Hence, by utilising the Tanh's rho function in the WMM estimator, the accuracy and the efficiency of the estimates can be improved substantially.

 

 

ABSTRAK

 

Makalah ini adalah mengenai pengembangan penganggaran regresi tak linear berheteroskedastik menggunakan fungsi Tanh psi. Ciri keteguhan bagi penggangar Tanh dan Hampel Berpemberat MM (WMM) diselidiki. Dalam kajian simulasi, didapati bahawa kepincangan dan RMSE bagi anggaran Hampel menokok lebih tinggi daripada anggaran Tanh apabila peratusan titik terpencil bertambah. Dengan yang demikian, apabila fungsi rho Tanh digunakan dalam penganggaran WMM, kejituan dan keberkesanan anggaran tersebut boleh dipertingkatkan.

 

 

RUJUKAN/REFERENCES

 

Carroll, R.J. & Ruppert, D. 1982. Robust Estimation in Heteroscedastic Linear Models. Ann. Stat. 10: 429-441.

Carroll, RJ. & Ruppert. D. 1998. Transformation and Weighting in Regression. London: Chapman and Hall.

Midi, H. 1999. Nonlinear Regression With Heteroscedastic Errors. Submitted to Science International 11(4).

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 & Sons.

Huber, PJ. 1981. Robust Statistics. New York: Wiley.

Neider, J. & Mead, R. 1965. A Simplex Method For Function Minimization. Computer J. 7: 308-313.

Press, W.H., Flannery, B.P., Teukolsky, S.A. & Vetterling, W.T. 1986. Numerical Recipes: The Art of Scientific Computing. New York: Cambridge University Press.

Rousseuw, PJ. 1984. Least Median of Squares Regression. J. Am. Stat. Assoc. 79: 871-879

Rousseuw, PJ. & Leroy, A. 1987. Robust Regresion and Outlier Detection. New York: Wiley.

Stromberg, AJ. 1992. High Breakdown Estimators In Nonlinear Regression. In Dodge, Y. (Ed.) L1-Statistical Analysis and Related Methods. 103-112. Amster­dam: North-Holland.

Stromberg, AJ 1993. Computational of High Breakdown Nonlinear Regression Parameters. J. Am. Stat. Assoc. 88(421): 237-244.

Yohai, V.J. 1987. High Breakdown-point And High Efficiency Robust Estimates for Regression. Ann. Statist. 15(20): 642-656.

 

 
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