kdevinecop: Kernel estimation of vine copula densities

Description

The function estimates a vine copula density using kernel estimators for the pair copulas (based on the kdecopula package).

Usage

kdevinecop(
  data,
  matrix = NA,
  method = "TLL2",
  renorm.iter = 3L,
  mult = 1,
  test.level = NA,
  trunc.level = NA,
  treecrit = "tau",
  cores = 1,
  info = FALSE
)

Value

An object of class kdevinecop. That is, a list containing

T1, T2, ...: lists of the estimted pair copulas in each tree,
matrix: the structure matrix of the vine,
info: additional information about the fit (if info = TRUE).

Arguments

data: (\(n x d\)) matrix of copula data (have to lie in \([0,1^d]\)).
matrix: R-Vine matrix (\(n x d\)) specifying the structure of the vine; if NA (default) the structure selection heuristic of Dissman et al. (2013) is applied.
method: see kdecop.
renorm.iter: see kdecop.
mult: see kdecop.
test.level: significance level for independence test. If you provide a number in \([0, 1]\), an independence test (BiCopIndTest) will be performed for each pair; if the null hypothesis of independence cannot be rejected, the independence copula will be set for this pair. If test.level = NA (default), no independence test will be performed.
trunc.level: integer; the truncation level. All pair copulas in trees above the truncation level will be set to independence.
treecrit: criterion for structure selection; defaults to "tau".
cores: integer; if cores > 1, estimation will be parallized within each tree (using foreach).
info: logical; if TRUE, additional information about the estimate will be gathered (see kdecop).

References

Nagler, T., Czado, C. (2016)
Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas.
Journal of Multivariate Analysis 151, 69-89 (doi:10.1016/j.jmva.2016.07.003)

Nagler, T., Schellhase, C. and Czado, C. (2017)
Nonparametric estimation of simplified vine copula models: comparison of methods arXiv:1701.00845

Dissmann, J., Brechmann, E. C., Czado, C., and Kurowicka, D. (2013).
Selecting and estimating regular vine copulae and application to financial returns.
Computational Statistics & Data Analysis, 59(0):52--69.

Examples

Run this code

data(wdbc, package = "kdecopula")
# rank-transform to copula data (margins are uniform)
u <- VineCopula::pobs(wdbc[, 5:7], ties = "average")
u <- u[1:30, ]
fit <- kdevinecop(u)                   # estimate density
dkdevinecop(c(0.1, 0.1, 0.1), fit)     # evaluate density estimate
contour(fit)                           # contour matrix (Gaussian scale)
pairs(rkdevinecop(500, fit))           # plot simulated data