Title: Smooth bootstrapping of copula functionals
Authors: Maximilian Coblenz - Karlsruhe Institute of Technology (Germany)
Oliver Grothe - Karlsruhe Institute of Technology (Germany)
Klaus Herrmann - Sherbrooke University (Canada) [presenting]
Marius Hofert - University of Waterloo (Canada)
Abstract: The smoothed bootstrap for functionals defined on the set (or possibly only a subset) of copulas is considered. Examples for such functionals include measures of association such as Kendall's tau or Spearmans' rho, the upper and lower tail dependence coefficients, or level sets that are used to quantify the risk inherent in joint events. The investigation is motivated by the question of how much the smoothing aspect of smoothed bootstrapping influences the underlying dependence structure in a multivariate framework. The strength of this dependence distortion may depend on the functional, the smoothing kernel or the sample size. We address these points with a special focus on elliptical distributions and smoothing kernels. While most motivating examples are bivariate in nature, the discussion is valid in arbitrary dimensions, making the results viable for high-dimensional settings and data science applications in general. A crucial part of multivariate kernel estimation, and hence of our algorithm, is the selection of a suitable bandwidth matrix. While the literature on bandwidth selection for multivariate kernel distribution function estimation has so far focused on special cases such as product kernels or diagonal bandwidth matrices, we present a novel cross-validation based approach that is valid for general bandwidth matrices.