A New Robust Method for Nonlinear Regression

Journal of Biometrics & Biostatistics

article

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

[1] School of Graduate Studies and Research, Meharry Medical College;Department of Mathematical Sciences, Cameron University;Department of Mathematics, New Jersey City University;Department of Medicine Division of Preventive Medicine and Comprehensive Cancer Center, University of Alabama Birmingham;Department of Pathology and Comprehensive Cancer Center, University of Alabama Birmingham

关键词: Robust nonlinear regression;    Least Square estimator;    Growth models;    Tumor size;    Metastasis;    Monte-carlo simulation;   

DOI  :  10.4172/2155-6180.1000199

来源: Hilaris Publisher

【 摘 要 】

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.

【 授权许可】

Unknown