Strong Approximation of Empirical Copula Processes by Gaussian Processes

TL;DR

This paper develops a strong approximation framework for empirical copula processes using Gaussian processes, including smoothed versions and a law of iterated logarithm, advancing statistical dependence modeling.

Contribution

It introduces a novel strong approximation method for empirical copula processes and their smoothed variants, along with a law of iterated logarithm, enhancing theoretical understanding.

Findings

Strong approximation of empirical copula processes by Gaussian processes.

Extension to smoothed empirical copula processes.

Establishment of a law of iterated logarithm for these processes.

Abstract

We provide the strong approximation of empirical copula processes by a Gaussian process. In addition we establish a strong approximation of the smoothed empirical copula processes and a law of iterated logarithm.