The release version on CRAN:

`install.packages("CondCopulas")`

The development version from GitHub, using the `devtools`

package:

```
# install.packages("devtools")
::install_github("AlexisDerumigny/CondCopulas") devtools
```

If you have any questions or suggestions, feel free to open an issue.

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.

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

`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 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

`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

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 \(Z\).

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 \(A\).

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