Smooth bootstrapping of copula functionals

TL;DR

This paper explores a smooth bootstrap method for estimating copula functionals in small samples, addressing key issues like domain boundaries and bandwidth selection, and analyzing its impact on dependence structures through examples and simulations.

Contribution

It introduces a novel smooth bootstrap approach for copula functionals, detailing how to implement it and analyzing its effects on dependence structures.

Findings

The method improves estimation accuracy in small samples.

Proper bandwidth selection is crucial for effective smoothing.

The approach preserves dependence structures under certain conditions.

Abstract

The smooth bootstrap for estimating copula functionals in small samples is investigated. It can be used both to gauge the distribution of the estimator in question and to augment the data. Issues arising from kernel density and distribution estimation in the copula domain are addressed, such as how to avoid the bounded domain, which bandwidth matrix to choose, and how the smoothing can be carried out. Furthermore, we investigate how the smooth bootstrap impacts the underlying dependence structure or the functionals in question and under which conditions it does not. We provide specific examples and simulations that highlight advantages and caveats of the approach.