tailDepFun (version 1.0.0)

stdfEmpCorr: 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.

Value

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

Details

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

References

Einmahl, J.H.J., Kiriliouk, A., and Segers, J. (2016). A continuous updating weighted least squares estimator of tail dependence in high dimensions. See http://arxiv.org/abs/1601.04826.

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)