How to install

From GitHub, using the devtools package:

devtools::install_github("AlexisDerumigny/CondCopulas")

Conditional copulas

With pointwise conditioning

Tests of the simplifying assumption

• 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

Estimation of conditional copulas (using kernel smoothing)

• 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

Estimation of conditional Kendall's tau (CKT)

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.

Kernel-based estimation of conditional Kendall's tau

• CKT.kernel: for any number of variable and with possible choice of the bandwidth

Kendall's regression

• CKT.kendallReg.fit: fit Kendall's regression, a regression-like method for the estimation of conditional Kendall's tau

• CKT.kendallReg.predict: for prediction of the new conditional Kendall's tau (given new covariates)

Classification-based estimation of conditional Kendall's tau

• using tree:

  • CKT.fit.tree: for fitting a tree-based model for the conditional Kendall's tau
  • CKT.predict.tree: for prediction of new conditional Kendall's taus

• using random forests:

  • CKT.fit.randomForest: for fitting a random forest-based model for the conditional Kendall's tau
  • CKT.predict.randomForest: for prediction of new conditional Kendall's taus

• using nearest neighbors:

  • CKT.predict.kNN: for several numbers of nearest neighbors

• using neural networks:

  • CKT.fit.nNets: for fitting a neural networks-based model for the conditional Kendall's tau
  • CKT.predict.nNets: for prediction of new conditional Kendall's taus

• using GLM:

  • CKT.fit.GLM: for fitting a GLM-like model for the conditional Kendall's tau
  • CKT.predict.GLM: for prediction of new conditional Kendall's taus

Advanced functions for manual hyperparameter choices

• CKT.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

With discrete conditioning by Borel sets

Test of the assumption that the conditioning Borel subset has no influence on the conditional copula

• bCond.simpA.param : assuming that the copula belongs to a parametric family

Estimation

• 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.

References

Derumigny, A., & Fermanian, J. D. (2017). About tests of the “simplifying” assumption for conditional copulas. Dependence Modeling, 5(1), 154-197.

Derumigny, A., & Fermanian, J. D. (2019). A classification point-of-view about conditional Kendall’s tau. Computational Statistics & Data Analysis, 135, 70-94.

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.

Derumigny, A., & Fermanian, J. D. (2020). On Kendall’s regression. Journal of Multivariate Analysis, 178, 104610.