About tests of the “simplifying” assumption for conditional copulas

Derumigny, Alexis; Fermanian, Jean David

doi:10.1515/demo-2017-0011

Cited by 30 publications

(54 citation statements)

References 51 publications

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“…The latter results will provide some simple tests of the constancy of the function z → τ 1,2|z , and then of the constancy of the associated conditional copula itself. This would test the famous "simplifying assumption" ("H 0 : C 1,2|Z=z does not depend on the choice of z"), a key assumption for vine modeling in particular: see [27] or [28] for a discussion, [29] for a review and a presentation of formal tests for this hypothesis.…”

Section: Asymptotic Behaviormentioning

confidence: 99%

On kernel-based estimation of conditional Kendall’s tau: finite-distance bounds and asymptotic behavior

Derumigny

Fermanian

2019

Dependence Modeling

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We study nonparametric estimators of conditional Kendall's tau, a measure of concordance between two random variables given some covariates. We prove non-asymptotic pointwise and uniform bounds, that hold with high probabilities. We provide "direct proofs" of the consistency and the asymptotic law of conditional Kendall's tau. A simulation study evaluates the numerical performance of such nonparametric estimators.

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Section: Asymptotic Behaviormentioning

confidence: 99%

On kernel-based estimation of conditional Kendall’s tau: finite-distance bounds and asymptotic behavior

Derumigny

Fermanian

2019

Dependence Modeling

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“…Mainly for practical reasons, some authors assume that the conditional copula of X given Z = z does not depend on z. This particular case is the so-called ''simplifying assumption'' (see, e.g., [9]), commonly used in vine models.…”

Section: Examplementioning

confidence: 99%

Single-index copulas

Fermanian

Lopez

2018

Journal of Multivariate Analysis

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We introduce so-called single-index copulas. They are semi-parametric conditional copulas whose parameter is an unknown link function of a univariate index only. We propose estimates of this link function and of the finite-dimensional unknown parameter. The asymptotic properties of the latter estimates are stated. Thanks to some properties of conditional Kendall's tau, we illustrate our technical conditions with several usual copula families.

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“…Considering the enormous number of scientific contributions working with and applying simplified pair-copulas (see, e.g., [5,6,7,32,36,38,37]) it is quite surprising that, apart from a few critical voices (see, e.g., [2,8,15]), no analytic and systematic study on the approximation quality and flexibility of these concepts seems to have been published so far.…”

Section: Introductionmentioning

confidence: 99%

How simplifying and flexible is the simplifying assumption in pair-copula constructions – analytic answers in dimension three and a glimpse beyond

Mroz

Fuchs

Trutschnig

2021

Electron. J. Statist.

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Motivated by the increasing popularity and the seemingly broad applicability of pair-copula constructions underlined by numerous publications in the last decade, in this contribution we tackle the unavoidable question on how flexible and simplifying the commonly used 'simplifying assumption' is from an analytic perspective and provide answers to two related open questions posed by Nagler and Czado in 2016. Aiming at a simplest possible setup for deriving the main results we first focus on the three-dimensional setting. We prove that the family of simplified copulas is flexible in the sense that it is dense in the set of all three-dimensional copulas with respect to the uniform metric d∞ -considering stronger notions of convergence like the one induced by the metric D 1 , by weak conditional convergence, by total variation, or by Kullback-Leibler divergence, however, the family even turns out to be nowhere dense and hence insufficient for any kind of flexible approximation. Furthermore, returning to d∞ we show that the partial vine copula is never the optimal simplified copula approximation of a given, non-simplified copula C, and derive examples illustrating that the corresponding approximation error can be strikingly large and extend to more than 28% of the diameter of the metric space. Moreover, the mapping ψ assigning each three-dimensional copula its unique partial vine copula turns out to be discontinuous with respect to d∞ (but continuous with respect to D 1 and to weak conditional convergence), implying a surprising sensitivity of partial vine copula approximations. The afore-mentioned main results concerning d∞ are then extended to the general multivariate setting.

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About tests of the “simplifying” assumption for conditional copulas

Cited by 30 publications

References 51 publications

On kernel-based estimation of conditional Kendall’s tau: finite-distance bounds and asymptotic behavior

On kernel-based estimation of conditional Kendall’s tau: finite-distance bounds and asymptotic behavior

Single-index copulas

How simplifying and flexible is the simplifying assumption in pair-copula constructions – analytic answers in dimension three and a glimpse beyond

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