Robust Estimation of Copulas by Maximum Mean Discrepancy

Provides functions for the robust estimation of parametric families of copulas using minimization of the Maximum Mean Discrepancy, following the article Alquier, Chérief-Abdellatif, Derumigny and Fermanian (2022) .

Package MMDCopula

This package implements the robust estimation procedure of copulas via maximum mean discrepancy (MMD), following the article Alquier, Chérief-Abdellatif, Derumigny, and Fermanian, J.D. (2022), Estimation of copulas via Maximum Mean Discrepancy. Journal of the American Statistical Association, doi:10.1080/01621459.2021.2024836.

How to install

The release version on CRAN:

install.packages("MMDCopula")

The development version from GitHub:

# install.packages("remotes")
remotes::install_github("AlexisDerumigny/MMDCopula")

Main functions

• BiCopEstMMD: estimate the parameter of a parametric bivariate copula by MMD minimization.

• BiCopConfIntMMD: compute a bootstrap-based or subsampling-based confidence interval for the parameter of a parametric bivariate copula.

• BiCopGradMMD: compute the gradient of the MMD criteria. Used in BiCopEstMMD.

Functions for simulation and inference for the Marshall-Olkin copula

• BiCopSim.MO: simulation of observations following a Marshall-Olkin copula.

• BiCopEst.MO: estimation of the parameter of a Marshall-Olkin copula.

• BiCopPar2Tau.MO and BiCopTau2Par.MO: convert between the parameter and the Kendall's tau of a Marshall-Olkin copula.

Other functions

• BiCopParamDistLp: compute the $L^p$ distance between two parametric copula models.