Solving estimating equations with copulas

TL;DR

This paper introduces a unified framework for solving estimating equations using copulas, enabling coherent inference across various regression problems with diverse data types and estimator methods.

Contribution

It generalizes copula-based estimation methods into a unified approach with theoretical guarantees and broad applicability.

Findings

Established consistency and asymptotic normality of estimators.

Validated bootstrap validity for inference.

Demonstrated versatility through simulations and financial application.

Abstract

Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical learning problems such as regression or classification. Framing such approaches as solutions of estimating equations, we generalize them in a unified framework. We can then obtain simultaneous, coherent inferences across multiple regression-like problems. We derive consistency, asymptotic normality, and validity of the bootstrap for corresponding estimators. The conditions allow for both continuous and discrete data as well as parametric, nonparametric, and semiparametric estimators of the copula and marginal distributions. The versatility of this methodology is illustrated by several theoretical examples, a simulation study, and an application to financial portfolio allocation.