Measuring association and dependence between random vectors

Grothe, Oliver; Schnieders, Julius; Segers, Johan

doi:10.1016/j.jmva.2013.08.019

Cited by 32 publications

(37 citation statements)

References 42 publications

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“…This measure of association between multivariate random vectors, along with others, is also discussed by Grothe et al. (). It however does not ensure that the closeness between grouped variables is monotone decreasing with increasing level of the merger.…”

Section: Inference For Hierarchical Kendall Copulasmentioning

confidence: 75%

Hierarchical Kendall copulas: Properties and inference

Brechmann

2014

Can J Statistics

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While there is substantial need for dependence models in higher dimensions, most existing models quickly become rather restrictive and barely balance parsimony and flexibility. Hierarchical constructions may improve on that by grouping variables in different levels. In this paper, the new class of hierarchical Kendall copulas is proposed and discussed. Hierarchical Kendall copulas are built up by flexible copulas specified for groups of variables, where aggregation is facilitated by the Kendall distribution function, the multivariate analog to the probability integral transform for univariate random variables. After deriving properties of the general model formulation, particular focus is given to inference techniques of hierarchical Kendall copulas with Archimedean components, for which closed‐form analytical expressions can be derived. A substantive application to German stock returns finally shows that hierarchical Kendall copulas perform very well for real data, out‐of‐ as well as in‐sample. The Canadian Journal of Statistics 42: 78–108; 2014 © 2014 Statistical Society of Canada

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Section: Inference For Hierarchical Kendall Copulasmentioning

confidence: 75%

Hierarchical Kendall copulas: Properties and inference

Brechmann

2014

Can J Statistics

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“…Markers whose association with the outcome lies between independence and comonotonicity are expected to exhibit useful discriminative and predictive properties. A way to quantify the association within ( M , T ), and consequently within ( M , D ), can be achieved by using Kendall's coefficient of concordance, tau, which is defined as 31

\begin{align} τ = cor (I_{false{M_{1} < M_{2} false}} false(m false), I_{false{T_{1} < T_{2} false}} false(t false)) = 4 \Pr false{M_{1} < M_{2}, T_{1} < T_{2} false} prefix- 1, \end{align}

where ( m , t ) ∈ (− ∞ , ∞ ) 2 and cor( X , Y ) is the correlation coefficient between the random variables X and Y ; here, the random vectors ( M 1 , T 1 ) and ( M 2 , T 2 ) are independent copies of ( M , T ). Kendall's tau is a popular nonparametric measure of ordinal association between M and T .…”

Section: Background and Methodsmentioning

confidence: 99%

Copula modeling of receiver operating characteristic and predictiveness curves

Escarela

Rodríguez

Núñez-Antonio

2020

Statistics in Medicine

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Receiver operating characteristic (ROC) and predictiveness curves are graphical tools to study the discriminative and predictive power of a continuous-valued marker in a binary outcome. In this paper, a copula-based construction of the joint density of the marker and the outcome is developed for plotting and analyzing both curves. The methodology only requires a copula function, the marginal distribution of the marker, and the prevalence rate for the model to be characterized. The adoption of the Gaussian copula and the customization of the margin for the marker are proposed for such characterization. The computation of both curves is numerically more feasible than methods that attempt to obtain one curve in terms of the other. Estimation is carried out using maximum likelihood and resampling-based methods. Randomized quantile residuals from each conditional distribution are employed for both assessing the adequacy of the model and identifying outliers. The performance of the estimators of both curves and their underlying quantities is evaluated in simulation studies that assume different dependence structures and sample sizes. The methods are illustrated with an analysis of the level of progesterone receptor gene expression for the diagnosis and prediction of estrogen receptor-positive breast cancer.

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“…As corresponding data, we use the well-known Merril Lynch government bond indices 46 for Germany (G0D0), Italy (G0I0), and Spain (G0E0) as in Grothe et al (2013).…”

Section: Description Of and The First Glance At Datamentioning

confidence: 99%

Corporate liquidity risk management: Coping with Corona and the clearing obligation

Lehrbass¹

2021

IJMRE

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The European Markets Infrastructure Regulation (EMIR) allows burdening a clearing obligation on non-financial corporations, which formerly did not necessarily clear their business. We give 10 recommendations on how to cope with this obligation. These are motivated by a case study for which we consider a stylized German power producer. For this entity, we derive optimal levels of planned production and forward sales of power using microeconomic theory. Since this results in a significant short position in the German power forward market, we investigate the resulting variation margin call dynamics with a special interest in the ability to forecast worst-case price up moves. We compare different models for the forward log-returns and their performance in 99% quantile forecasting. A GARCH model with Student-t distribution emerges as the most suitable model. This is used in the case study, which is inspired by data published by the power producer E.ON. Using recent material from the Basel Committee on Banking Supervision we distill the reliable liquidity buffer from an allegedly rich liquidity position and show how suddenly it can be eroded. We point to feedback loops, which make the challenges-posed by the clearing obligation-even more severe. We also spend some thoughts on how to cope with the crisis caused by Corona.

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Measuring association and dependence between random vectors

Cited by 32 publications

References 42 publications

Hierarchical Kendall copulas: Properties and inference

Hierarchical Kendall copulas: Properties and inference

Copula modeling of receiver operating characteristic and predictiveness curves

Corporate liquidity risk management: Coping with Corona and the clearing obligation

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