New algorithm for obtaining robust estimation of q-Gaussian regression models

This paper introduces a novel q-Gaussian regression model, leveraging the flexibility of the q-Gaussian distribution Nq(m,σ2) to provide a more adaptable modeling approach than traditional Gaussian regression. We establish sufficient conditions for the asymptotic normality of the model’s estimators and present a new algorithm for parameter estimation. Our methodology, which combines moment estimation and maximum likelihood techniques, is validated through numerical experiments and demonstrated on a real-world water infiltration dataset, showcasing its strong performance.