The release version on CRAN:
install.packages("CondCopulas")
The development version from GitHub, using the devtools package:
# install.packages("devtools")
devtools::install_github("AlexisDerumigny/CondCopulas")
If you have any questions or suggestions, feel free to open an issue.
Conditional copulas with pointwise conditioningIn this first part, we are interesting in the inference of the conditional copula of a random vector $X$ given the pointwise conditioning $Z = z$ , where $Z$ is another random vector and $z$ is a fixed value.
Tests of the simplifying assumptionThese functions perform a test of the "simplifying assumption" that the conditional copula $C_{X | Z = z}$ does not depend on the value of $z$ .
simpA.NP: in a purely nonparametric framework
simpA.param: assuming that the conditional copula belongs to a parametric family of copulas for all values of the conditioning variable
simpA.kendallReg: test of the simplifying assumption based on the constancy of the conditional Kendall's tau assuming that it satisfies a regression-like equation
These functions estimate the conditional copula $C_{X | Z = z}$ in different frameworks.
estimateNPCondCopula: nonparametric estimation of conditional copulas.
estimateParCondCopula: parametric estimation of conditional copulas.
estimateParCondCopula_ZIJ: parametric estimation of conditional copulas using (already computed) conditional pseudo-observations.
In this part, we assume that the dimension of $X$ is $2$ , i.e. $X = (X_1, X_2)$ . Instead of estimating the conditional copula $C_{X | Z = z}$ which is an infinite-dimensional object for every value of $z$ , it is possible to estimate the conditional Kendall's tau (CKT) $\tau_{1,2|Z=z}$ which is a real number in $[-1, 1]$ for every value of $z$ .
To estimate the conditional Kendall's tau, the package provides a general wrapper function:
CKT.estimate: that can be used for any method of estimating conditional Kendall's tau. Each of these methods is detailed below and has its own function.CKT.kernel: use kernel smoothing to estimate the conditional Kendall's tau. The bandwidth can be given by the user or determined by cross-validation.CKT.kendallReg.fit: fit Kendall's regression, a regression-like method for the estimation of conditional Kendall's tau.
CKT.kendallReg.predict: predict the conditional Kendall's tau given new values $z$ of the covariates.
using tree:
CKT.fit.tree: for fitting a tree-based model for the conditional Kendall's tauCKT.predict.tree: for prediction of new conditional Kendall's taususing random forests:
CKT.fit.randomForest: for fitting a random forest-based model for the conditional Kendall's tauCKT.predict.randomForest: for prediction of new conditional Kendall's taususing nearest neighbors:
CKT.predict.kNN: for several numbers of nearest neighborsusing neural networks:
CKT.fit.nNets: for fitting a neural networks-based model for the conditional Kendall's tauCKT.predict.nNets: for prediction of new conditional Kendall's taususing GLM:
CKT.fit.GLM: for fitting a GLM-like model for the conditional Kendall's tauCKT.predict.GLM: for prediction of new conditional Kendall's tausCKT.hCV.Kfolds: for K-fold cross-validation choice of the bandwidth for kernel smoothing
CKT.hCV.l1out: for leave-one-out cross-validation choice of the bandwidth for kernel smoothing
CKT.KendallReg.LambdaCV : cross-validated choice of the penalization parameter lambda
CKT.adaptkNN: for a (local) aggregation of the number of nearest neighbors based on Lepski's method
In this second part, we are interesting in the inference of the conditional copula of a random vector $X$ given the discrete conditioning $Z \in A$ , where $Z$ is another random vector and $A$ is a Borel subset of possible values of $Z$ .
Test of the hypothesis that the conditioning Borel subset has no influence on the conditional copulaThese functions perform a test of the hypothesis that the conditional copula $C_{X | Z \in A}$ does not depend on the value of $A$ for different choices of the conditioning set $A$ .
bCond.simpA.param : test of this hypothesis, assuming that the copula belongs to a parametric family
bCond.simpA.CKT: test of the hypothesis that conditional Kendall's tau are equal over all the different conditioning subsets.
bCond.pobs : computation of the conditional pseudo-observations $F_{1|A(i)}(X_{i,1} | A(i))$ and $F_{2|A(i)}(X_{i,2} | A(i))$ for every $i=1, \dots, n$ .
bCond.estParamCopula : estimation of a conditional parametric copula, i.e. for every set $A$ , a conditional parameter $\theta(A)$ is estimated.
bCond.treeCKT: construction of binary tree whose leaves corresponds to the most relevant conditioning subsets (in the sense of maximizing the difference between estimated conditional Kendall's taus).Derumigny, A., & Fermanian, J. D. (2017). About tests of the “simplifying” assumption for conditional copulas. Dependence Modeling, 5(1), 154-197. pdf
Derumigny, A., & Fermanian, J. D. (2019). A classification point-of-view about conditional Kendall’s tau. Computational Statistics & Data Analysis, 135, 70-94. pdf
Derumigny, A., & Fermanian, J. D. (2019). On kernel-based estimation of conditional Kendall’s tau: finite-distance bounds and asymptotic behavior. Dependence Modeling, 7(1), 292-321. pdf
Derumigny, A., & Fermanian, J. D. (2020). On Kendall’s regression. Journal of Multivariate Analysis, 178, 104610. pdf
Derumigny, A., & Fermanian, J. D. (2022). Conditional empirical copula processes and generalized dependence measures. Electronic Journal of Statistics, 16(2), 5692-5719. pdf
Derumigny, A., Fermanian, J. D., & Min, A. (2022). Testing for equality between conditional copulas given discretized conditioning events. Canadian Journal of Statistics. pdf
van der Spek, R., & Derumigny, A. (2025). Fast estimation of Kendall’s Tau and conditional Kendall’s Tau matrices under structural assumptions. Dependence Modeling, 13(1), 20250012. pdf
Derumigny, A. (2025). Measures of non-simplifyingness for conditional copulas and vines. arXiv:2504.07704
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