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Confidence Regions for Multivariate Quantiles

Coblenz, Maximilian 1; Dyckerhoff, Rainer; Grothe, Oliver 1
1 Institut für Operations Research (IOR), Karlsruher Institut für Technologie (KIT)


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.

Verlagsausgabe §
DOI: 10.5445/IR/1000085950
Veröffentlicht am 24.09.2018
DOI: 10.3390/w10080996
Zitationen: 3
Web of Science
Zitationen: 3
Zitationen: 5
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Operations Research (IOR)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2018
Sprache Englisch
Identifikator ISSN: 2073-4441
KITopen-ID: 1000085950
Erschienen in Water
Verlag MDPI
Band 10
Heft 8
Seiten Article: 996
Bemerkung zur Veröffentlichung This article belongs to the Special Issue Advances in Multivariate Analysis of Environmental Phenomena: Celebrating the 15th Anniversary of Copulas in Hydrology.
Gefördert durch den KIT-Publikationsfonds
Vorab online veröffentlicht am 27.07.2018
Schlagwörter confidence regions; copulas; hydrology; level set estimation; multivariate quantiles
Nachgewiesen in Web of Science
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