# Weak convergence of the weighted empirical beta copula process

## TL;DR

This paper proves the weak convergence of the weighted empirical beta copula process, enhancing the theoretical foundation for dependence modeling and simplifying applications in statistical tests and dependence function estimation.

## Contribution

It establishes the weak convergence of the weighted empirical beta copula process, providing a stronger and more straightforward tool than previous results for dependence analysis.

## Key findings

- Weak convergence of the weighted empirical beta copula process.
- Application to weighted independence tests.
- Improved estimation of the Pickands dependence function.

## Abstract

The empirical copula has proved to be useful in the construction and understanding of many statistical procedures related to dependence within random vectors. The empirical beta copula is a smoothed version of the empirical copula that enjoys better finite-sample properties. At the core lie fundamental results on the weak convergence of the empirical copula and empirical beta copula processes. Their scope of application can be increased by considering weighted versions of these processes. In this paper we show weak convergence for the weighted empirical beta copula process. The weak convergence result for the weighted empirical beta copula process is stronger than the one for the empirical copula and its use is more straightforward. The simplicity of its application is illustrated for weighted Cram\'er--von Mises tests for independence and for the estimation of the Pickands dependence function of an extreme-value copula.