CondCopulas (version 0.2.0)

estimateNPCondCopula: Compute a kernel-based estimator of the conditional copula

Description

Assuming that we observe a sample \((X_{i,1}, X_{i,2}, X_{i,3}), i=1, \dots, n\), this function returns a array \(\hat C_{1,2|3}(u_1, u_2 | X_3 = x_3)\) for each choice of (u_1, u_2, x_3).

Usage

estimateNPCondCopula(
  X1 = NULL,
  X2 = NULL,
  X3 = NULL,
  U1_,
  U2_,
  newX3,
  kernel,
  h,
  observedX1 = NULL,
  observedX2 = NULL,
  observedX3 = NULL
)

Value

An array of dimension (length(U1_, U2_, newX3))

whose element in position (i, j, k) is \(\hat C_{1,2|3}(u_1, u_2 | X_3 = x_3)\)

where \(u_1\) = U1_[i], \(u_2\) = U2_[j] and \(x_3\) = newX3[k]

Arguments

X1, X2, X3

vectors of observations of size n

U1_

a vector of numbers in [0, 1]

U2_

a vector of numbers in [0, 1]

newX3

a vector of new values for the conditioning variable X3

kernel

a character string describing the kernel to be used. Possible choices are Gaussian, Triangular and Epanechnikov.

h

the bandwidth to use in the estimation.

observedX1, observedX2, observedX3

old parameter names for X1, X2, X3. Support for this will be removed at a later version.

References

Derumigny, A., & Fermanian, J. D. (2017). About tests of the “simplifying” assumption for conditional copulas. Dependence Modeling, 5(1), 154-197. tools:::Rd_expr_doi("10.1515/demo-2017-0011")

See Also

estimateParCondCopula for estimating a conditional copula in a parametric setting ( = where the conditional copula is assumed to belong to a parametric class). simpA.NP for a test that this conditional copula is constant with respect to the value \(x_3\) of the conditioning variable.

Examples

# We simulate from a conditional copula
N = 500
X3 = rnorm(n = N, mean = 5, sd = 2)
conditionalTau = 0.9 * pnorm(X3, mean = 5, sd = 2)
simCopula = VineCopula::BiCopSim(N=N , family = 3,
    par = VineCopula::BiCopTau2Par(1 , conditionalTau ))
X1 = qnorm(simCopula[,1])
X2 = qnorm(simCopula[,2])

# We do the estimation
grid = c(0.2, 0.4, 0.6, 0.8)
arrayEst = estimateNPCondCopula(
  X1 = X1, X2 = X2, X3 = X3,
  U1_ = grid, U2_ = grid, newX3 = c(2, 5, 7),
  kernel = "Gaussian", h = 0.8)
arrayEst