BiCopConfIntMMD: Confidence intervals for the estimated parameter of a...

In MMDCopula: Robust Estimation of Copulas by Maximum Mean Discrepancy

Confidence intervals for the estimated parameter of a bivariate parametric copula using MMD estimation

Description

Confidence intervals for the estimated parameter of a bivariate parametric copula using MMD estimation

Usage

BiCopConfIntMMD(
  x1,
  x2,
  family,
  nResampling = 100,
  subsamplingSize = length(x1),
  corrSubSampling = TRUE,
  level = 0.95,
  ...
)

Arguments

x1	vector of observations of the first coordinate.
x2	vector of observations of the second coordinate.
family	parametric family of copulas. Supported families are: 1: Gaussian copulas 3: Clayton copulas 4: Gumbel copulas 5: Frank copulas MO: Marshall-Olkin copulas
nResampling	number of resampling times.
subsamplingSize	size of the subsample. By default it is length(u1), i.e. this corresponds to the nonparametric boostrap.
corrSubSampling	this parameter is only used for subsampling-based confidence intervals. If TRUE, the confidence interval uses the corrected subsample empirical process.
level	the nominal confidence level.
...	other parameters to be given to BiCopEstMMD or BiCopEst.MO.

Value

a list with the confidence intervals CI.Tau for Kendall's tau and CI.Par for the corresponding parameter.

References

Alquier, P., Chérief-Abdellatif, B.-E., Derumigny, A., and Fermanian, J.D. (2022). Estimation of copulas via Maximum Mean Discrepancy. Journal of the American Statistical Association, doi: 10.1080/01621459.2021.2024836.

Kojadinovic I., and Stemikovskaya, K. (2019) Subsampling (weighted smooth) empirical copula processes. Journal of Multivariate Analysis, 173, 704-723, doi: 10.1016/j.jmva.2019.05.007.

Examples

data = VineCopula::BiCopSim(N = 50, family = 1, par = 0.3)
result = BiCopConfIntMMD(x1 = data[,1], x2 = data[,2], family = 1,
  nResampling = 2, subsamplingSize = 10, niter = 10)

data_ = VineCopula::BiCopSim(N = 1000, family = 1, par = 0.3)
result_ = BiCopConfIntMMD(x1 = data_[,1], x2 = data_[,2], family = 1)
result_$CI.Tau
result_$CI.Par

MMDCopula documentation built on April 25, 2022, 5:06 p.m.