stdfEmpCorr {tailDepFun}

Bias-corrected empirical stable tail dependence function

Description

Returns the bias-corrected stable tail dependence function in dimension d, evaluated in a point cst.

Usage

stdfEmpCorr(
  ranks,
  k,
  cst = rep(1, ncol(ranks)),
  tau = 5,
  k1 = (nrow(ranks) - 10)
)

Arguments

ranks

A n x d matrix, where each column is a permutation of the integers 1:n, representing the ranks computed from a sample of size n.

k

An integer between 1 and n - 1; the threshold parameter in the definition of the empirical stable tail dependence function.

cst

The value in which the tail dependence function is evaluated: defaults to rep(1,d).

tau

The parameter of the power kernel. Defaults to 5.

k1

An integer between 1 and n; defaults to n - 10.

Details

The values for k1 and tau are chosen as recommended in Beirlant et al. (2016). This function might be slow for large n.

Value

A scalar between \max(x_1,\ldots,x_d) and x_1 + \cdots + x_d.

References

Einmahl, J.H.J., Kiriliouk, A., and Segers, J. (2018). A continuous updating weighted least squares estimator of tail dependence in high dimensions. Extremes 21(2), 205-233.

Beirlant, J., Escobar-Bach, M., Goegebeur, Y., and Guillou, A. (2016). Bias-corrected estimation of stable tail dependence function. Journal of Multivariate Analysis, 143, 453-466.

See Also

stdfEmp

Examples

## Simulate data from the Gumbel copula
set.seed(2)
cop <- copula::gumbelCopula(param = 2, dim = 4)
data <- copula::rCopula(n = 1000, copula = cop)
stdfEmpCorr(apply(data,2,rank), k = 50)