Kernel Smoothing for Bivariate Copula Densities
This package provides fast implementations of kernel estimators for the copula density. Due to its several plotting options it is particularly useful for the exploratory analysis of dependence structures. It can be further used for flexible nonparametric estimation of copula densities and resampling.
The function kdecop can be used to estimate a copula density
with a number of popular kernel estimators. The density estimate can be
evaluated on arbitrary points with dkdecop;
the cdf with pkdecop. Furthermore, synthetic
data can be simulated with rkdecop, and
several plot options are provided by
plot.kdecopula.
Thomas Nagler
Nagler, T. (2018)
kdecopula: An R Package for the Kernel Estimation of Bivariate Copula
Densities.
Journal of Statistical Software 84(7), 1-22
Gijbels, I. and Mielniczuk, J. (1990).
Estimating the density of a copula function.
Communications in Statistics - Theory and Methods, 19(2):445-464.
Charpentier, A., Fermanian, J.-D., and Scaillet, O. (2006).
The estimation of copulas: Theory and practice.
In Rank, J., editor, Copulas: From theory to application in finance. Risk Books.
Geenens, G., Charpentier, A., and Paindaveine, D. (2017).
Probit transformation for nonparametric kernel estimation of the copula
density.
Bernoulli, 23(3), 1848-1873.
Nagler, T. (2014).
Kernel Methods for Vine Copula Estimation.
Master's Thesis, Technische Universitaet Muenchen,
https://mediatum.ub.tum.de/node?id=1231221
Wen, K. and Wu, X. (2015).
Transformation-Kernel Estimation of the Copula Density,
Working paper,
http://agecon2.tamu.edu/people/faculty/wu-ximing/agecon2/public/copula.pdf
## load data and transform with empirical cdf data(wdbc) udat <- apply(wdbc[, -1], 2, function(x) rank(x)/(length(x)+1)) ## estimation of copula density of variables 5 and 6 dens.est <- kdecop(udat[, 5:6]) plot(dens.est) ## evaluate density estimate at (u1,u2)=(0.123,0.321) dkdecop(c(0.123, 0.321), dens.est) ## evaluate cdf estimate at (u1,u2)=(0.123,0.321) pkdecop(c(0.123, 0.321), dens.est) ## simulate 500 samples from density estimate rkdecop(500, dens.est)
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