BiCopConfIntMMD {MMDCopula}

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