measures_nonsimplifyingness_NP: Compute a measure of non-simplifyingness based on non-parametric estimation of the conditional copula

Description

Compute a measure of non-simplifyingness based on non-parametric estimation of the conditional copula

Usage

measures_nonsimplifyingness_NP(
  X1,
  X2,
  Z,
  h,
  measures = "all",
  kernel.name = "Epanechnikov",
  truncVal = NULL,
  numericalInt = list(kind = "legendre", nGrid = 10),
  verbose = 0
)

Value

a data.frame where each row corresponds to one measure of non-simplifyingness and one choice of h. As a particular case, if measures and h are both of length 1, this data.frame will have only one row.

Arguments

X1, X2

vector of n observations of the conditioned variables

Z

vector of n observations of the conditioning variable

h

the bandwidth used for kernel smoothing

measures

choices of measures of non-simplifyingness to be computed. measures = "all" includes all available non-parametric measures of non-simplifyingness. Otherwise, measures must be a character vector and a subset of c("T1_CvM_Cs3", "T1_CvM_Cs4", "tilde_T0_CvM", "T1_KS_Cs3", "T1_KS_Cs4", "tilde_T0_KS").

kernel.name

the name of the kernel

truncVal

the value of truncation for the integral, i.e. the integrals are computed from truncVal to 1-truncVal instead of from 0 to 1. Note that truncVal must be in the interval \([0, 0.5)\), i.e. \(0\) is allowed but not \(0.5\).

The default is truncVal = NULL, which actually means that truncVal = h if h < 0.5 and truncVal = 0 else.

numericalInt

parameters to be given to statmod::gauss.quad, including the number of quadrature points and the type of interpolation.

verbose

option used for debugging. If verbose = 0, the function is silent. Higher values of verbose give more explicit details on the computations.

References

Derumigny, A. (2025). Measures of non-simplifyingness for conditional copulas and vines. ArXiv preprint, arXiv:2504.07704. tools:::Rd_expr_doi("10.48550/arXiv.2504.07704")

Examples

Run this code

set.seed(1)
N = 500
Z = rnorm(n = N, mean = 5, sd = 2)
conditionalTau = 0.8
simCopula = VineCopula::BiCopSim(N=N , family = 1,
    par = VineCopula::BiCopTau2Par(1 , conditionalTau ))
X1 = qnorm(simCopula[,1], mean = Z)
X2 = qnorm(simCopula[,2], mean = - Z)

result <- measures_nonsimplifyingness_NP(
   X1 = X1, X2 = X2, Z = Z, h = 0.08, measures = "tilde_T0_CvM")

result <- measures_nonsimplifyingness_NP(
   X1 = X1, X2 = X2, Z = Z, h = 0.08, measures = "all")