A new approach using the genetic algorithm for parameter estimation in multiple linear regression with long-tailed symmetric distributed error terms: An application to the Covid-19 data

Abdullah Yalçınkaya; İklim Gedik Balay; Birdal Şenoǧlu

doi:10.1016/j.chemolab.2021.104372

A new approach using the genetic algorithm for parameter estimation in multiple linear regression with long-tailed symmetric distributed error terms: An application to the Covid-19 data

Chemometr Intell Lab Syst. 2021 Sep 15:216:104372. doi: 10.1016/j.chemolab.2021.104372. Epub 2021 Jun 29.

Authors

Abdullah Yalçınkaya¹, İklim Gedik Balay², Birdal Şenoǧlu¹

Affiliations

¹ Department of Statistics, Ankara University, 06100, Ankara, Turkey.
² Business School, Ankara Yıldırım Beyazıt University, 06760, Ankara, Turkey.

Abstract

Maximum likelihood (ML) estimators of the model parameters in multiple linear regression are obtained using genetic algorithm (GA) when the distribution of the error terms is long-tailed symmetric. We compare the efficiencies of the ML estimators obtained using GA with the corresponding ML estimators obtained using other iterative techniques via an extensive Monte Carlo simulation study. Robust confidence intervals based on modified ML estimators are used as the search space in GA. Our simulation study shows that GA outperforms traditional algorithms in most cases. Therefore, we suggest using GA to obtain the ML estimates of the multiple linear regression model parameters when the distribution of the error terms is LTS. Finally, real data of the Covid-19 pandemic, a global health crisis in early 2020, is presented for illustrative purposes.

Keywords: Genetic algorithm; Long-tailed symmetric distribution; Maximum likelihood; Modified maximum likelihood; Multiple linear regression.