Detecting outliers when fitting data with nonlinear regression - a new method based on robust nonlinear regression...

Area of Science:

• Biostatistics
• Data Analysis
• Scientific Computing

Background:

• Nonlinear regression typically assumes Gaussian data scatter, aiming to minimize sum-of-squares.
• Outliers can significantly skew nonlinear regression results by dominating calculations.
• Existing practical methods for routine outlier identification in nonlinear regression are limited.

Purpose of the Study:

• To develop a practical and reliable method for identifying outliers in nonlinear regression analysis.
• To improve the accuracy and robustness of curve fitting when data may contain outliers.

Main Methods:

• Introduced a novel robust nonlinear regression technique assuming Lorentzian distribution for data scatter.
• Developed an adaptive method that increases robustness during the fitting process.
• Adapted the false discovery rate approach for outlier definition and implemented outlier removal before ordinary least-squares regression, termed the ROUT method.

Main Results:

• The ROUT method demonstrated a low false positive rate (1-3%) on simulated Gaussian data.
• Effective outlier identification was achieved on contaminated data, with an average False Discovery Rate below 1%.
• The combined robust regression and outlier removal approach proved effective.

Conclusions:

• The developed ROUT method successfully identifies outliers in nonlinear curve fitting.
• The method offers a balance of statistical power and a low rate of false positives.
• This approach enhances the reliability of nonlinear regression analysis in the presence of outliers.