EstimationBR {tailDepFun} | R Documentation |
Estimation of the parameters of the Brown-Resnick process
Description
Estimation the parameters of the Brown-Resnick process, using either the pairwise M-estimator or weighted least squares (WLS).
Usage
EstimationBR(
x,
locations,
indices,
k,
method,
isotropic = FALSE,
biascorr = FALSE,
Tol = 1e-05,
k1 = (nrow(x) - 10),
tau = 5,
startingValue = NULL,
Omega = diag(nrow(indices)),
iterate = FALSE,
covMat = TRUE
)
Arguments
x |
An |
locations |
A |
indices |
A |
k |
An integer between 1 and |
method |
Choose between |
isotropic |
A Boolean variable. If |
biascorr |
For |
Tol |
For |
k1 |
For |
tau |
For |
startingValue |
Initial value of the parameters in the minimization routine. Defaults to |
Omega |
A |
iterate |
A Boolean variable. If |
covMat |
A Boolean variable. If |
Details
The parameters of the Brown-Resnick process are either (\alpha,\rho)
for an isotropic process or (\alpha,\rho,\beta,c)
for an anisotropic process. The matrix indices
can be either user-defined or returned from the function selectGrid
with cst = c(0,1)
. Estimation might be rather slow when iterate = TRUE
or even when covMat = TRUE
.
Value
A list with the following components:
theta | The estimator using the optimal weight matrix. |
theta_pilot | The estimator without the optimal weight matrix. |
covMatrix | The estimated covariance matrix for the estimator. |
value | The value of the minimized function at theta . |
References
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.
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.
See Also
Examples
## define the locations of 9 stations
locations <- cbind(rep(c(1:3), each = 3), rep(1:3, 3))
## select the pairs of locations
indices <- selectGrid(cst = c(0,1), d = 9, locations = locations, maxDistance = 1.5)
## The Brown-Resnick process
set.seed(1)
x <- SpatialExtremes::rmaxstab(n = 1000, coord = locations, cov.mod = "brown",
range = 3, smooth = 1)
## Calculate the estimtors.
EstimationBR(x, locations, indices, 100, method = "Mestimator", isotropic = TRUE,
covMat = FALSE)$theta
EstimationBR(x, locations, indices, 100, method = "WLS", isotropic = TRUE,
covMat = FALSE)$theta