stdfEmp {tailDepFun}

Empirical stable tail dependence function

Description

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

Usage

stdfEmp(ranks, k, cst = rep(1, ncol(ranks)))

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), i.e., the extremal coefficient.

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.

See Also

stdfEmpCorr

Examples

## Simulate data from the Gumbel copula and compute the extremal coefficient in dimension four.
set.seed(2)
cop <- copula::gumbelCopula(param = 2, dim = 4)
data <- copula::rCopula(n = 1000, copula = cop)
stdfEmp(apply(data,2,rank), k = 50)