Modeling Multivariate Distributions with Continuous Margins Using the copula R Package

By Ivan Kojadinovic, Jun Yan. 2010

437 citations recorded by the source corpus.

The copula-based modeling of multivariate distributions with continuous margins is presented as a succession of rank-based tests: a multivariate test of randomness followed by a test of mutual independence and a series of goodness-of-fit tests. All the tests under consideration are based on the empirical copula, which is a nonparametric rank-based estimator of the true unknown copula. The principles of the tests are recalled and their implementation in the copula R package is briefly described. Their use in the construction of a copula model from data is thoroughly illustrated on real insurance and financial data.

Subfields: Finance, Global and Planetary Change, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/847a138fca499e07160e315d1e70cb2b4aaee9f7

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Citations in the corpus

Selection strategies for regular vine copulae (2013, methodology): “The corresponding implementation in the statistical software R is described in [Kojadinovic and Yan, 2010].”
Dependence between high sea-level and high river discharge increases flood hazard in global deltas and estuaries (2018, methodology): “We use the maximum pseudo-likelihood estimator (Kojadinovic and Yan 2010) to calculate parameters for three different copulas: Gumbel (upper tail dependence), Frank (no tail dependence), and Clayton (lower tail dependence).”
Analysis of directional dependence using asymmetric copula-based regression models (2014, background): “Note that Kojadinovic and Yan [37] verified that the randomization (designed to randomly break the ties) does not change the results for the copula inference.”
Multivariate return period calculation via survival functions (2013, methodology): “A freeware package written for ‘‘R’’ is available online for working with copulas [see Kojadinovic and Yan, 2010].”
Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine (2013, methodology): “For MLE standard errors are based on inversion of the Hessian matrix, while for inversion of Kendall’s τ they are obtained as described in Kojadinovic and Yan (2010a).”
Large‐sample tests of extreme‐value dependence for multivariate copulas (2011, methodology): “Note finally that all the tests studied in this work are implemented in the R package copula (Kojadinovic and Yan, 2010) available on the Comprehensive R Archive Network (R Development Core Team, 2011).”
FAST LARGE-SAMPLE GOODNESS-OF-FIT TESTS FOR COPULAS (2011, positive): “As demonstrated in Kojadinovic and Yan (2010b), ignoring the ties, by using for instance mid-ranks in the computation of the pseudo-observations, may affect the results qualitatively.”
Upper tail dependence in rainfall extremes: would we know it if we saw it? (2015, methodology): “where CN denotes the empirical survival copula (Nelsen 2006, pp. 32–34), 1 f g is the indicator function, R1;i and R2;i denote the ranks of x1;i and x2;i, for i 1⁄4 1; . . .;N, and j a threshold rank to be chosen by using for instance the heuristic plateau-finding algorithm described by Schmidt (200”
Selection of Vine Copulas (2013, methodology): “Corresponding p-values are calculated using fast bootstrap methods based on the multiplier approach developed and implemented in [39, 40, 41].”
A goodness-of-fit test for bivariate extreme-value copulas (2011, background): “For example, many studies have concluded that a Gumbel–Hougaard copula structure is adequate for the insurance data mentioned in the Introduction; see, for instance, [5, 8, 9, 11, 15, 16] or [27].”
Derivation of low flow distribution functions using copulas (2014, methodology): “The Cramér-von Mises Sn statistics based on the difference between empirical and theoretical copulas (Genest and Rémillard, 2008; Genest et al., 2009; Kojadinovic and Yan, 2010) are also shown in Table 3, including the corresponding P values.”
Multivariate multiparameter extreme value models and return periods: A copula approach (2010, methodology): “[30] In particular, the copulas used in the case study analyzed in section 5 can be easily investigated and simulated via a package written for “R” [Yan and Kojadinovic, 2009; Kojadinovic and Yan, 2010b], or by the procedure described by Salvadori et al. [2007, Appendix A.2].”