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Conditional normal extreme-value copulas. (English) Zbl 1475.62163

Summary: We propose a new class of extreme-value copulas which are extreme-value limits of conditional normal models. Conditional normal models are generalizations of conditional independence models, where the dependence among observed variables is modeled using one unobserved factor. Conditional on this factor, the distribution of these variables is given by the Gaussian copula. This structure allows one to build flexible and parsimonious models for data with complex dependence structures, such as data with spatial dependence or factor structure. We study the extreme-value limits of these models and show some interesting special cases of the proposed class of copulas. We develop estimation methods for the proposed models and conduct a simulation study to assess the performance of these algorithms. Finally, we apply these copula models to analyze data on monthly wind maxima and stock return minima.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
60G70 Extreme value theory; extremal stochastic processes
62P20 Applications of statistics to economics
62P35 Applications of statistics to physics

Software:

CopulaModel
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References:

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