An estimator of the stable tail dependence function based on the empirical beta copula

TL;DR

This paper introduces a smoothed estimator for the stable tail dependence function using integrated beta kernels, which improves finite-sample performance while maintaining the same asymptotic properties, and leverages the empirical beta copula for resampling.

Contribution

The paper proposes a novel smoothed estimator based on integrated beta kernels that enhances finite-sample performance and simplifies resampling via the empirical beta copula.

Findings

The new estimator has superior finite-sample performance.

It retains the same asymptotic distribution as the original estimator.

A simple resampling scheme is derived from the connection with the empirical beta copula.

Abstract

The replacement of indicator functions by integrated beta kernels in the definition of the empirical stable tail dependence function is shown to produce a smoothed version of the latter estimator with the same asymptotic distribution but superior finite-sample performance. The link of the new estimator with the empirical beta copula enables a simple but effective resampling scheme.