Description Usage Arguments Details Value Author(s) References Examples
View source: R/gradient_score.R
Compute the peaks-over-threshold gradient score function for the Brown–Resnick model.
1 2 3 4 5 6 7 8 9 10 | scoreEstimation(
obs,
loc,
vario,
weightFun = NULL,
dWeightFun = NULL,
nCores = 1L,
cl = NULL,
...
)
|
obs |
List of vectors exceeding an R-threshold, see de Fondeville and Davison (2018) for more details. |
loc |
Matrix of coordinates as given by |
vario |
Semi-variogram function taking a vector of coordinates as input. |
weightFun |
Function of weights. |
dWeightFun |
Partial derivative function of |
nCores |
Number of cores used for the computation |
cl |
Cluster instance as created by |
... |
Parameters for |
The function computes the gradient score based on the representation developed by Wadsworth et al. (2014). Margins must have been standardized. The weighting function must be differentiable and verify some properties for consistency, see de Fondeville and Davison (2018) for more details.
Evaluation of the gradient score function for the set of observations obs
and semi-variogram vario
.
Raphael de Fondeville
de Fondeville, R. and Davison A. (2018). High-dimensional peaks-over-threshold inference. Biometrika, 105(3), 575-592.
Wadsworth, J. L. and J. A. Tawn (2014). Efficient inference for spatial extreme value processes associated to log-Gaussian random functions. Biometrika, 101(1), 1-15.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | #Define variogram function
vario <- function(h){
1 / 2 * norm(h,type = "2")^1.5
}
#Define locations
loc <- expand.grid(1:4, 1:4)
#Simulate data
obs <- simulPareto(1000, loc, vario)
#Evaluate risk functional
sums <- sapply(obs, sum)
#Define weighting function
weightFun <- function(x, u){
x * (1 - exp(-(sum(x / u) - 1)))
}
#Define partial derivative of weighting function
dWeightFun <- function(x, u){
(1 - exp(-(sum(x / u) - 1))) + (x / u) * exp( - (sum(x / u) - 1))
}
#Select exceedances
threshold <- quantile(sums, 0.9)
exceedances <- obs[sums > threshold]
#Evaluate gradient score function
scoreEstimation(exceedances, loc, vario, weightFun = weightFun, dWeightFun, u = threshold)
|
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