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Water 2018, 10(8), 996; https://doi.org/10.3390/w10080996

Confidence Regions for Multivariate Quantiles

1
Karlsruhe Institute of Technologie (KIT), Institute of Operations Research, 76131 Karlsruhe, Germany
2
Institute of Econometrics and Statistics, University of Cologne, 50923 Cologne, Germany
*
Author to whom correspondence should be addressed.
Received: 26 June 2018 / Revised: 20 July 2018 / Accepted: 25 July 2018 / Published: 27 July 2018
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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 focus on two recently developed approaches to estimate confidence regions for level sets and extend them to provide confidence regions for multivariate quantiles based on copulas. In a simulation study, we check coverage probabilities of the employed approaches. In particular, we focus on small sample sizes. One approach shows reasonable coverage probabilities and the second one obtains mixed results. 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. View Full-Text
Keywords: confidence regions; copulas; hydrology; level set estimation; multivariate quantiles confidence regions; copulas; hydrology; level set estimation; multivariate quantiles
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Coblenz, M.; Dyckerhoff, R.; Grothe, O. Confidence Regions for Multivariate Quantiles. Water 2018, 10, 996.

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