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.
The third author gratefully acknowledges financial support of the Karlsruhe Institute of Technology (KIT) where part of this research was carried out. The third author would like to thank NSERC for financial support for this work through Discovery Grant RGPIN-2020-05784. The fourth author acknowledges support from NSERC through grants RGPIN-2020-04897 and RGPAS-2020-00093.
We thank an anonymous reviewer for helpful comments which improved the quality of the paper.
"Smooth bootstrapping of copula functionals." Electron. J. Statist. 16 (1) 2550 - 2606, 2022. https://doi.org/10.1214/22-EJS2007