Title: Confidence regions for multivariate quantiles
Authors: Maximilian Coblenz - Karlsruhe Institute of Technology (Germany) [presenting]
Rainer Dyckerhoff - University of Cologne (Germany)
Oliver Grothe - Karlsruhe Institute of Technology (Germany)
Abstract: Multivariate quantiles are of increasing importance in applications of hydrology. This calls for reliable methods to evaluate the precision of the estimated quantile sets. Therefore, we investigate two recently developed approaches to estimate confidence regions for level sets. These are extended to multivariate quantiles based on copulas. In a simulation study we check coverage probabilities of the employed approaches. A focus is on small sample sizes. Overall, the adapted approaches show reasonable coverage probabilities. However, not only the bounded copula domain but also the additional estimation of the quantile level pose some problems. A small sample application gives further insight into the employed techniques.