On non-central squared copulas. (English) Zbl 1440.62189

Summary: The goal of this paper is to introduce new families of multivariate copulas, extending the chi-square copulas, the Fisher copula, and squared copulas. The new families are constructed from existing copulas by first transforming their margins to standard Gaussian distributions, then transforming these variables into non-central chi-square variables with one degree of freedom, and finally by considering the copula associated with these new variables. It is shown that by varying the non-centrality parameters, one can model non-monotonic dependence, and when one or many non-centrality parameters are outside a given hyper-rectangle, then the copula is almost the same as the one when these parameters are infinite. For these new families, the tail behavior, the monotonicity of dependence measures such as Kendall’s tau and Spearman’s rho are investigated, and estimation is discussed. The R package NCSCopula [the author, “NCSCopula: non-central squared copula models estimation”, R package version 1.0.1 (2019)] can be used to estimate the parameters for several copula families.


62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H12 Estimation in multivariate analysis


R; CDVine; NCSCopula
Full Text: DOI


[1] Bárdossy, A., Copula-based geostatistical models for groundwater quality parameters, Water Resour. Res., 42, 11 (2006)
[2] Brechmann, E.; Schepsmeier, U., Modeling dependence with C- and D-Vine copulas: The R package CDVine, J. Stat. Softw. Artic., 52, 3, 1-27 (2013)
[3] Demarta, S.; McNeil, A. J., The t copula and related copulas, Internat. Statist. Rev., 73, 1, 111-129 (2005) · Zbl 1104.62060
[4] Dette, H.; VanHecke, R.; Volgushev, S., Some comments on copula-based regression, J. Amer. Statist. Assoc., 109, 507, 1319-1324 (2014) · Zbl 1368.62094
[5] Favre, A.-C.; Quessy, J.-F.; Toupin, M.-H., The new family of Fisher copulas to model upper tail dependence and radial asymmetry: Properties and application to high-dimensional rainfall data, Environmetrics, 29, 3, 2494 (2018)
[6] Genest, C.; Ghoudi, K.; Rivest, L.-P., A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika, 82, 543-552 (1995) · Zbl 0831.62030
[7] Nasri, B. R., NCSCopula: Non-Central Squared Copula Models Estimation (2019), R package version 1.0.1
[8] Nasri, B. R.; Rémillard, B. N.; Bouezmarni, T., Semi-parametric copula-based models under non-stationarity, J. Multivariate Anal., 173, 347-365 (2019) · Zbl 1422.62189
[9] Nelsen, R. B., (An Introduction to Copulas. An Introduction to Copulas, Lecture Notes in Statistics, vol. 139 (2006), Springer-Verlag: Springer-Verlag New York) · Zbl 1152.62030
[10] Oh, D. H.; Patton, A. J., High-dimensional copula-based distributions with mixed frequency data, J. Econometrics, 193, 2, 349-366 (2016) · Zbl 1431.62657
[11] Quessy, J.-F.; Durocher, M., The class of copulas arising from squared distributions: properties and inference, Econom. Stat., 12, 148-166 (2019)
[12] Quessy, J.-F.; Rivest, L.-P.; Toupin, M.-H., On the family of multivariate chi-square copulas, J. Multivariate Anal., 152, 40-60 (2016) · Zbl 1349.62179
[13] Shih, J. H.; Louis, T. A., Inferences on the association parameter in copula models for bivariate survival data, Biometrics, 51, 1384-1399 (1995) · Zbl 0869.62083
[14] Varin, C.; Reid, N.; Firth, D., An overview of composite likelihood methods, Statist. Sinica, 5-42 (2011) · Zbl 05849508
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.