A novel perspective for parameter estimation of seemingly unrelated nonlinear regression

Area of Science:

• Statistics
• Mathematical Modeling

Background:

• Nonlinear regression models relationships between variables with nonlinear patterns.
• Seemingly unrelated nonlinear regression (SUNR) accounts for correlations in multi-response datasets.
• Traditional SUNR parameter estimation relies on the L2-norm based nonlinear least squares (NLS) method.

Purpose of the Study:

• To introduce a novel multi-objective SUNR (MO-SUNR) model.
• To integrate the L1-norm based least absolute deviation (LAD) method with the NLS method for parameter estimation.
• To explore alternative parameter estimation strategies for SUNR models.

Main Methods:

• Development of the multi-objective SUNR (MO-SUNR) model.
• Simultaneous application of LAD (L1-norm) and NLS (L2-norm) for parameter estimation.
• Utilizing soft computing methods for MO-SUNR model optimization.

Main Results:

• The MO-SUNR model successfully integrates LAD and NLS methods.
• Demonstrated applicability of the MO-SUNR model using two real-world datasets.
• The MO-SUNR approach yields multiple, usable compromise parameter estimates.

Conclusions:

• The MO-SUNR framework provides a flexible approach to parameter estimation in nonlinear regression.
• Simultaneous consideration of different norms (L1 and L2) enhances modeling capabilities.
• This method offers valuable alternatives for analyzing correlated multi-response data.