# How to install

The release version on CRAN:

install.packages("CondCopulas")

From GitHub, using the devtools package:

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

# 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.