AsymVarBR {tailDepFun}

Asymptotic variance matrix for the Brown-Resnick process.

Description

Computes the asymptotic variance matrix for the Brown-Resnick process, estimated using the pairwise M-estimator or the weighted least squares estimator.

Usage

AsymVarBR(locations, indices, par, method, Tol = 1e-05)

Arguments

locations

A d x 2 matrix containing the Cartesian coordinates of d points in the plane.

indices

A q x d matrix containing exactly 2 ones per row, representing a pair of points from the matrix locations, and zeroes elsewhere.

par

The parameters of the Brown-Resnick process. Either (\alpha,\rho) for an isotropic process or (\alpha,\rho,\beta,c) for an anisotropic process.

method

Choose between "Mestimator" and "WLS".

Tol

For "Mestimator" only. The tolerance in the numerical integration procedure. Defaults to 1e-05.

Details

The parameters of a The matrix indices can be either user-defined or returned from the function selectGrid with cst = c(0,1). Calculation might be rather slow for method = "Mestimator".

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

locations <- cbind(rep(1:2, 3), rep(1:3, each = 2))
indices <- selectGrid(cst = c(0,1), d = 6, locations = locations, maxDistance = 1)
AsymVarBR(locations, indices, par = c(1.5,3), method = "WLS")