Exploring the Application of Copula-Based Regression Models in Capturing Nonlinear Dependence Structures

Posted: Oct 02, 2014

• Caleb Ross
• Caroline Foster
• Carter Bell

Abstract

Traditional regression methodologies have long served as foundational tools in statistical analysis across numerous disciplines. However, these approaches frequently rely on assumptions that may not align with the complex realities of modern datasets. The presumption of linear relationships, homoscedastic errors, and multivariate normality often proves inadequate when confronting the intricate dependence structures present in real-world phenomena. This limitation becomes particularly pronounced in domains such as finance, environmental science, and healthcare, where variables frequently exhibit nonlinear associations, asymmetric dependencies, and tail behavior that defies Gaussian assumptions. The copula framework, introduced by Sklar in 1959, offers a promising alternative by providing a mechanism to separate the modeling of marginal distributions from the dependence structure between variables. While copulas have found substantial application in financial risk management and extreme value theory, their integration into regression frameworks remains relatively unexplored. This paper addresses this gap by developing a comprehensive copula-based regression methodology that explicitly models complex dependence patterns while maintaining flexibility in marginal distribution specification.