datasetPairs: Construct a dataset of pairs of observations for the estimation of conditional Kendall's tau

Description

In (Derumigny, & Fermanian (2019)), it is described how the problem of estimating conditional Kendall's tau can be rewritten as a classification task for a dataset of pairs (of observations). This function computes such a dataset, that can be then used to estimate conditional Kendall's tau using one of the following functions: CKT.fit.tree, CKT.fit.randomForest, CKT.fit.GLM, CKT.fit.nNets, CKT.predict.kNN.

Usage

datasetPairs(
  X1,
  X2,
  Z,
  h,
  cut = 0.9,
  onlyConsecutivePairs = FALSE,
  nPairs = NULL
)

Value

A matrix with (4+dimZ) columns and n*(n-1)/2 rows if onlyConsecutivePairs=FALSE and else (n/2) rows. It is structured in the following way:

column 1 contains the information about the concordance of the pair (i,j) ;
columns 2 to 1+dimZ contain the mean value of Z (the conditioning variables) ;
column 2+dimZ contains the value of the kernel K_h(Z_j - Z_i) ;
column 3+dimZ and 4+dimZ contain the corresponding values of i and j.

Arguments

X1: vector of observations of the first conditioned variable.
X2: vector of observations of the second conditioned variable.
Z: vector or matrix of observations of the conditioning variable(s), of dimension dimZ.
h: the bandwidth. Can be a vector; in this case, the components of h will be reused to match the dimension of Z.
cut: the cutting level to keep a given pair or not. Used only if no nPairs is provided.
onlyConsecutivePairs: if TRUE, only consecutive pairs are used.
nPairs: number of most relevant pairs to keep in the final datasets. If this is different than the default NULL, the cutting level cut is not used.

References

Derumigny, A., & Fermanian, J. D. (2019). A classification point-of-view about conditional Kendall’s tau. Computational Statistics & Data Analysis, 135, 70-94. (Algorithm 1 for all pairs and Algorithm 8 for the case of only consecutive pairs) tools:::Rd_expr_doi("10.1016/j.csda.2019.01.013")

Examples

Run this code

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

datasetP = datasetPairs(
X1 = X1, X2 = X2, Z = Z, h = 0.07, cut = 0.9)