Smooth bootstrapping of copula functionals

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 in-vestigate 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 advan-tages and caveats of the approach.