On the length of copula level curves

Coblenz, Maximilian; Grothe, Oliver; Schreyer, Manuela; Trutschnig, Wolfgang

doi:10.1016/j.jmva.2018.06.001

Cited by 2 publications

(1 citation statement)

References 19 publications

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“…Furthermore, the shape of the boundary is determined by the shape of the level curve of the copula. The level curve reflects the distribution of the probability mass and the strength of dependence between the involved variables (see, e.g., [28]) which transfers to the quantile definition here. For further motivation and theoretical considerations of this approach, see [7,10].…”

Section: Definition 1 ([9]mentioning

confidence: 99%

Confidence Regions for Multivariate Quantiles

Coblenz

Dyckerhoff

Grothe

2018

Water

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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.

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Section: Definition 1 ([9]mentioning

confidence: 99%

Confidence Regions for Multivariate Quantiles

Coblenz

Dyckerhoff

Grothe

2018

Water

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A link between Kendall’s τ, the length measure and the surface of bivariate copulas, and a consequence to copulas with self-similar support

Sánchez,

Trutschnig

2023

Dependence Modeling

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Working with shuffles, we establish a close link between Kendall’s τ \tau , the so-called length measure, and the surface area of bivariate copulas and derive some consequences. While it is well known that Spearman’s ρ \rho of a bivariate copula A A is a rescaled version of the volume of the area under the graph of A A , in this contribution we show that the other famous concordance measure, Kendall’s τ \tau , allows for a simple geometric interpretation as well – it is inextricably linked to the surface area of A A .

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On the length of copula level curves

Cited by 2 publications

References 19 publications

Confidence Regions for Multivariate Quantiles

Confidence Regions for Multivariate Quantiles

A link between Kendall’s τ, the length measure and the surface of bivariate copulas, and a consequence to copulas with self-similar support

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