On the covariance of the asymptotic empirical copula process

TL;DR

This paper investigates the asymptotic covariance properties of the empirical copula process, showing conditions under which it has smaller covariance than the standard empirical process, with implications for statistical inference.

Contribution

It provides new conditions under which the empirical copula process exhibits reduced asymptotic covariance, enhancing understanding of its inferential properties.

Findings

Empirical copula process can have smaller asymptotic covariance than standard empirical process.

Conditions for covariance reduction are explicitly characterized.

Implications for improved statistical inference are discussed.

Abstract

Conditions are given under which the empirical copula process associated with a random sample from a bivariate continuous distribution has a smaller asymptotic covariance function than the standard empirical process based on observations from the copula. Illustrations are provided and consequences for inference are outlined.