How to install

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 conditioning

In 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 assumption

These functions perform a test of the “simplifying assumption” that the conditional copula \(C_{X | Z = z}\) does not depend on the value of \(z\).

Estimation of conditional copulas (using kernel smoothing)

These functions estimate the conditional copula \(C_{X | Z = z}\) in different frameworks.

Estimation of conditional Kendall’s tau (CKT)

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:

Kernel-based estimation of conditional Kendall’s tau

Kendall’s regression

Classification-based estimation of conditional Kendall’s tau

Advanced functions for manual hyperparameter choices

Conditional copulas with discrete conditioning by Borel sets

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 copula

These 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 \(A\).

Estimation

Data-driven choice of conditioning subsets

References

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. (2022). Fast estimation of Kendall’s Tau and conditional Kendall’s Tau matrices under structural assumptions. arXiv:2204.03285.