The likelihood and Bayesian analyses for asymmetric Laplace nonlinear regression model

• Published in: Computational & applied mathematics 2024-02, Vol.43 (1), Article 21
• Main Authors: Gilani, Narjes, Pourmousa, Reza
• Format: Article
• Language: English
• Subjects: Algorithms; Applications of Mathematics; Bayesian analysis; Computational Mathematics and Numerical Analysis; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Maximum likelihood estimates; Outliers (statistics); Parameter estimation; Regression models; Skewed distributions
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-023-02528-y

Regression model is a popular and well-acknowledged technique for finding a relationship between random phenomena. In this context, the normality assumption on the error terms is one of the challenging issues in practical studies because many phenomena in the real world are prone to skewness, peakness, and outliers. In this paper, a new generalization of nonlinear regression models is postulated by considering asymmetric Laplace distribution on the error terms to cover the drawbacks of the normal-based model in accommodating skew data with peakness and mild outliers. We present three stochastic representations of the model which enables us to develop an expectation–maximization (EM) algorithm to computationally obtain the maximum-likelihood (ML) parameter estimates. The observed information matrix is computed by adopting an information-based approach. The Bayesian analysis for the proposed model is also investigated. Finally, experiments on the simulation and real-world datasets illustrate some computational and robust aspects of the proposed model.