title: A New Robust Method for Nonlinear Regression.
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.
  
  
  METHODS
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: School of Graduate Studies and Research, Meharry Medical College, Nashville, TN 37208, USA.
authors.forename: M A
authors.initials: MA
authors.lastname: Tabatabai
authors.affiliation: Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA.
authors.forename: J J
authors.initials: JJ
authors.lastname: Kengwoung-Keumo
authors.affiliation: Department of Mathematics, New Jersey City University, Jersey City, NJ 07305, USA.
authors.forename: W M
authors.initials: WM
authors.lastname: Eby
authors.affiliation: Department of Medicine Division of Preventive Medicine and Comprehensive Cancer Center, University of Alabama Birmingham, Birmingham, AL 35294, USA.
authors.forename: S
authors.initials: S
authors.lastname: Bae
authors.affiliation: Department of Pathology and Comprehensive Cancer Center, University of Alabama Birmingham, Birmingham, AL 35294, USA.
authors.forename: U
authors.initials: U
authors.lastname: Manne
authors.affiliation: Department of Medicine Division of Preventive Medicine and Comprehensive Cancer Center, University of Alabama Birmingham, Birmingham, AL 35294, USA.
authors.forename: M
authors.initials: M
authors.lastname: Fouad
authors.affiliation: Department of Medicine Division of Preventive Medicine and Comprehensive Cancer Center, University of Alabama Birmingham, Birmingham, AL 35294, USA.
authors.forename: K P
authors.initials: KP
authors.lastname: Singh
keywords: Growth models; Least Square estimator; Metastasis; Monte-carlo simulation; Robust nonlinear regression; Tumor size