AsymVarGumbel {tailDepFun}

Asymptotic variance matrix for the Gumbel model.

Description

Computes the asymptotic variance matrix for the Gumbel model, estimated using the pairwise M-estimator or the weighted least squares estimator.

Usage

AsymVarGumbel(indices, par, method)

Arguments

indices

A q x d matrix containing at least 2 non-zero elements per row, representing the values in which we will evaluate the stable tail dependence function. For method = Mestimator, this matrix should contain exactly two ones per row.

par

The parameter of the Gumbel model.

method

Choose between "Mestimator" and "WLS".

Details

The matrix indices can be either user defines or returned by selectGrid. For method = "Mestimator", only a grid with exactly two ones per row is accepted, representing the pairs to be used.

Value

A q by q matrix.

References

Einmahl, J.H.J., Kiriliouk, A., Krajina, A., and Segers, J. (2016). An Mestimator of spatial tail dependence. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 78(1), 275-298.

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

selectGrid

Examples

indices <- selectGrid(c(0,1), d = 3, nonzero = c(2,3))
AsymVarGumbel(indices, par = 0.7, method = "WLS")