A new approach using the genetic algorithm for parameter estimation in multiple linear regression with long-tailed...

Area of Science:

• Statistics
• Computational Statistics
• Regression Analysis

Background:

• Maximum likelihood (ML) estimation is crucial for parameter estimation in multiple linear regression.
• Traditional iterative methods may struggle with long-tailed symmetric error distributions.
• Robustness in statistical modeling is essential for real-world data analysis.

Purpose of the Study:

• To investigate the efficacy of genetic algorithms (GA) for obtaining ML estimators in multiple linear regression.
• To compare the performance of GA-based ML estimators against traditional iterative techniques.
• To apply the developed method to analyze real-world data, such as Covid-19 pandemic data.

Main Methods:

• Utilizing genetic algorithms (GA) to find maximum likelihood (ML) estimators.
• Employing Monte Carlo simulation studies to compare estimator efficiencies.
• Incorporating robust confidence intervals based on modified ML estimators within the GA search space.
• Applying the methodology to analyze real-world Covid-19 pandemic data.

Main Results:

• Genetic algorithms (GA) demonstrate superior performance in obtaining ML estimators compared to traditional algorithms in most tested scenarios.
• The efficiency of GA-based ML estimators is validated through extensive Monte Carlo simulations.
• The study confirms the effectiveness of GA for multiple linear regression with long-tailed symmetric error distributions.

Conclusions:

• Genetic algorithms (GA) are recommended for estimating parameters in multiple linear regression models when error terms follow a long-tailed symmetric distribution.
• The proposed GA approach offers a robust and efficient alternative to conventional methods.
• The methodology is applicable to analyzing complex datasets, including those from global health crises like the Covid-19 pandemic.