An Overview of the Goodness-of-Fit Test Problem for Copulas

Fermanian, Jean‐David

doi:10.1007/978-3-642-35407-6_4

Cited by 26 publications

(11 citation statements)

References 93 publications

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“…In statistical theory, the obtained result about absolutely continuous copulas suggests that this assumption is somehow too strong. Novel procedures are called for (especially in various goodness-of-fit tests [9]) to extend their setting to a larger class of copulas.…”

Section: Discussionmentioning

confidence: 99%

A typical copula is singular

Durante

Sánchez

Trutschnig

2015

Journal of Mathematical Analysis and Applications

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We present Baire category results in the class of bivariate copulas (or, equivalently, doubly stochastic probability measures) endowed with two different metrics under which the space is complete. Main content of the paper is that, in the sense of Baire categories with respect to the topology induced by the uniform metric, the family of absolutely continuous copulas is of first category, whereas the family of purely singular copulas is co-meager and, hence, of second category. Moreover, several other popular dense sub-classes of copulas are considered, like shuffles of Min and checkerboard copulas.

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Section: Discussionmentioning

confidence: 99%

A typical copula is singular

Durante

Sánchez

Trutschnig

2015

Journal of Mathematical Analysis and Applications

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“…But this approach revealed good results in the comparison study of Genest et al (2009) for bivariate copulas. Further suggestions for copula GOF tests are for example presented in Fermanian (2012).…”

Section: Discussionmentioning

confidence: 99%

“…Along with the break through of vine copula constructions model diagnosis becomes ever so imperative in the application of multi-dimensional vine copulas. Developing efficient GOF tests is now a timely task as already noted in Fermanian (2012), and an important addition to the current literature of vine copulas. In addition, comprehensive comparisons for many of the classical GOF tests are lacking in terms of their relative merits when they are applied to multi-dimensional copulas.…”

Section: Introductionmentioning

confidence: 99%

A goodness-of-fit test for regular vine copula models

Schepsmeier

2016

Econometric Reviews

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We introduce a new goodness-of-fit test for regular vine (R-vine) copula models. R-vine copulas are a very flexible class of multivariate copulas based on a pair-copula construction (PCC). The test arises from the information matrix equality and specification test proposed by White (1982) and extends the goodness-of-fit test for copulas introduced by Huang and Prokhorov (2013). The corresponding critical value can be approximated by asymptotic theory or simulation. The simulation based test shows excellent performance with regard to observed size and power in an extensive simulation study, while the asymptotic theory based test is inaccurate for n ≤ 10000 for a 5-dimensional model (in d = 8 even 20000 are not enough). The simulation based test is applied to select among different R-vine specifications to model the dependency among exchange rates.

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“…Empirical copula processes play the same role for copulas as empirical processes for distribution functions and they have been extensively used in goodness-of-fit testing problems for copulas (see Fermanian (2013) for an overview about this subject). Several works have been devoted to discuss the asymptotic behaviour of C n in (4.2).…”

Section: Copulasmentioning

confidence: 99%

Directional differentiability for supremum-type functionals: Statistical applications

Cárcamo¹,

Cuevas²,

Rodríguez³

2020

Bernoulli

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We show that various functionals related to the supremum of a real function defined on an arbitrary set or a measure space are Hadamard directionally differentiable. We specifically consider the supremum norm, the supremum, the infimum, and the amplitude of a function. The (usually non-linear) derivatives of these maps adopt simple expressions under suitable assumptions on the underlying space. As an application, we improve and extend to the multidimensional case the results in Raghavachari (1973) regarding the limiting distributions of Kolmogorov-Smirnov type statistics under the alternative hypothesis. Similar results are obtained for analogous statistics associated with copulas. We additionally solve an open problem about the Berk-Jones statistic proposed by Jager and Wellner (2004). Finally, the asymptotic distribution of maximum mean discrepancies over Donsker classes of functions is derived.

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An Overview of the Goodness-of-Fit Test Problem for Copulas

Cited by 26 publications

References 93 publications

A typical copula is singular

A typical copula is singular

A goodness-of-fit test for regular vine copula models

Directional differentiability for supremum-type functionals: Statistical applications

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