Hybrid Copula Estimators

TL;DR

This paper introduces a hybrid copula estimator that combines different estimators for joint and marginal distributions, useful when extra information or assumptions are available, supported by a functional central limit theorem.

Contribution

It develops a new hybrid estimator for copulas that integrates various marginal estimators, extending the empirical copula framework with theoretical validation.

Findings

Establishes a functional central limit theorem for the hybrid estimator

Provides examples demonstrating the estimator's application and properties

Shows improved flexibility in modeling copulas with additional marginal information

Abstract

An extension of the empirical copula is considered by combining an estimator of a multivariate cumulative distribution function with estimators of the marginal cumulative distribution functions for marginal estimators that are not necessarily equal to the margins of the joint estimator. Such a hybrid estimator may be reasonable when there is additional information available for some margins in the form of additional data or stronger modelling assumptions. A functional central limit theorem is established and some examples are developed.