Title: Nonparametric estimation of multivariate quantiles in small sample sizes
Authors: Oliver Grothe - Karlsruhe Institute of Technology (Germany)
Rainer Dyckerhoff - University of Cologne (Germany)
Maximilian Coblenz - Karlsruhe Institute of Technology (Germany) [presenting]
Abstract: In many applications, quantiles provide important insights in the statistical problems considered. We focus on the estimation of multivariate quantiles based on copulas. We provide a nonparametric estimation procedure for a specific notion of multivariate quantiles which is in particular useful for applications in hydrology. These quantiles are based on level sets of copulas and admit the usual probabilistic interpretation that a p-quantile comprises a probability mass p. We design a smoothed bootstrap procedure to cope with the typically small sample sizes expected in hydrology. We show that, in particular for extreme events with return periods of 30 years and more, the proposed procedure highly improves precision and accuracy of the estimation results compared to base line approaches.