Function tailIntEmp

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Description

Integral of the bivariate empirical stable tail dependence function over the unit square.

Usage

1
tailIntEmp(ranks, n = nrow(ranks), k)

Arguments

ranks

A n x 2 matrix, where each column is a permutation of the integers 1:n, representing the ranks computed from a sample of size n.

n

The sample size. If not specified, it is computed as the number of rows of the matrix ranks.

k

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

Details

This is an analytic implementation of the integral of the stable tail dependence function, which is much faster than numerical integration. See Einmahl et al. (2014) for a definition of the empirical stable tail dependence function.

Value

A scalar.

References

Einmahl, J.H.J., Kiriliouk, A., Krajina, A. and Segers, J. (2014), "An M-estimator of spatial tail dependence". See http://arxiv.org/abs/1403.1975.

See Also

Mestimator, tailInt

Examples

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n <- 20
(ranks <- cbind(sample(1:n), sample(1:n)))
tailIntEmp(ranks, k = 5)