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ISSN: 2155-6180

Journal of Biometrics & Biostatistics
Open Access

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Research Article

A New Robust Method for Nonlinear Regression

Tabatabai MA1, Kengwoung-Keumo JJ2, Eby WM3, Bae S4, Manne U5, Fouad M4 and Singh KP4*

1School of Graduate Studies and Research, Meharry Medical College, Nashville, TN 37208, USA

2Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

3Department of Mathematics, New Jersey City University, Jersey City, NJ 07305, USA

4Department of Medicine Division of Preventive Medicine and Comprehensive Cancer Center, University of Alabama Birmingham, Birmingham, AL 35294, USA

5Department of Pathology and Comprehensive Cancer Center, University of Alabama Birmingham, Birmingham, AL 35294, USA

*Corresponding Author:
Singh KP
Department of Medicine Division of Preventive Medicine and Comprehensive Cancer Center
University of Alabama Birmingham, Birmingham, AL 35294, USA
Tel: +205-934-6887
E-mail: [email protected]

Received date: June 30, 2014; Accepted date: September 10, 2014; Published date: September 18, 2014

Citation: Tabatabai MA, Kengwoung-Keumo JJ, Eby WM, Bae S, Manne U, et al. (2014) A New Robust Method for Nonlinear Regression. J Biom Biostat 5:199. doi: 10.4172/2155-6180.1000199

Copyright: © 2014 Tabatabai MA, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are are credited.

Abstract

Background: When outliers are present, the least squares method of nonlinear regression performs poorly. The main purpose of this paper is to provide a robust alternative technique to the Ordinary Least Squares nonlinear regression method. This new robust nonlinear regression method can provide accurate parameter estimates when outliers and/or influential observations are present.

Method: Real and simulated data for drug concentration and tumor size-metastasis are used to assess the performance of this new estimator. Monte Carlo simulations are performed to evaluate the robustness of our new method in comparison with the Ordinary Least Squares method.

Results: In simulated data with outliers, this new estimator of regression parameters seems to outperform the Ordinary Least Squares with respect to bias, mean squared errors, and mean estimated parameters. Two algorithms have been proposed. Additionally and for the sake of computational ease and illustration, a Mathematica program has been provided in the Appendix.

Conclusion: The accuracy of our robust technique is superior to that of the Ordinary Least Squares. The robustness and simplicity of computations make this new technique more appropriate and useful tool for the analysis of nonlinear regressions.

Keywords

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