spectralLikelihood {mvPot}

Spectral log-likelihood function

Description

Compute the negative spectral log-likelihood function for Brown–Resnick model with peaks-over-threshold.

Usage

spectralLikelihood(obs, loc, vario, nCores = 1L, cl = NULL)

Arguments

obs

List of observations vectors for which sum(x) exceeds a high threshold.

loc

Matrix of coordinates as given by expand.grid().

vario

Semi-variogram function taking a vector of coordinates as input.

nCores

Number of cores used for the computation

cl

Cluster instance as created by makeCluster of the parallel package.

Details

The function compute the negative log-likelihood function based on the spectral representation developed by Engelke et al. (2015). This simplified expression is obtained by conditioning on the event 'sum(x) exceeds a high threshold u > 1'. Margins must have been standardized.

Value

Negative spectral log-likelihood function evaluated at the set of observations obs with semi-variogram vario.

References

Engelke, S. et al. (2015). Estimation of Huesler-Reiss distributions and Brown-Resnick processes. Journal of the Royal Statistical Society: Series B, 77(1), 239-265

Examples

#Define semi-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)

#Select exceedances
exceedances <- obs[sums > quantile(sums, 0.9)]

#Evaluate the spectral function
spectralLikelihood(exceedances, loc, vario)