tailDepFun (version 1.0.0)

AsymVarBR: 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.

Value

A q by q matrix.

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".

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. (2016). A continuous updating weighted least squares estimator of tail dependence in high dimensions. See http://arxiv.org/abs/1601.04826.

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")