nllHT: Negative log-likelihood for bivariate Heffernan and Tawn...

In Jbrich95/sdfExtreme: Spatial Deformation for Non-Stationary Extremal Dependence

Negative log-likelihood for bivariate Heffernan and Tawn (2004) model

Description

Calculates the negative log-likelihood for Y|X=x. This is a profile log-likelihood with free parameters α and β. We use the same normalising functions as in the original paper.

Usage

nllHT(X, Y, par)

Arguments

X	Vector of Laplace variables. This is the conditioning variable i.e. X=x.
Y	Vector of Laplace variables, Y.
par	Vector (α,β).

Value

Negative log-likelihood for Heffernan and Tawn model fit to Y|X=x.

References

Heffernan and Tawn (2004), Journal of the Royal Statistical Society: Series B, 66:497-546, (doi)

Examples

#For a N by d matrix of data "Z" and d by 2 matrix of coordinates "Gcoords".
# We use data(Aus_Heat) as an example.

library(rmutil)
library(fields)
data(Aus_Heat) 
Z<-Aus_Heat$Temp.
Gcoords<-Aus_Heat$coords

unif<-function(x) rank(x)/(length(x)+1)
Z_U<-Z
for(i in 1:dim(Z_U)[2]) Z_U[,i]<-unif(Z[,i]) # Transform to uniform margins
Z_LP<-qlaplace(Z_U) # Transform to Laplace margins


p<-dim(Gcoords)[1]
ConExp<-matrix(0,nrow=p,ncol=p)

u<-quantile(Z_LP,0.98) #Quantile for estimating conditional expectation

#Calculate conditional expectation for each pair
for(i in 1:p){
 for(j in 1:i){
   Exceedances<-cbind(Z_LP[,i],Z_LP[,j])[which(Z_LP[,i]>=u),]
   opt<-optim(nllHT,X=Exceedances[,1],Y=Exceedances[,2],par=c(0.3,0.8))
   #print(opt)
   alpha<-opt$par[1]
   beta<-opt$par[2]
  mu<-mean((Exceedances[,2]-alpha*Exceedances[,1])/Exceedances[,1]^beta)
  ConExp[i,j]<-alpha*u+u^beta*mu
}

}
ConExp<-ConExp+t(ConExp)  ##Symmetry assumed
diag(ConExp)<-diag(ConExp)/2

plot(rdist.earth(Gcoords,miles=F),ConExp, ylab="Conditional Expectation",
    xlab="Distance (Km)", main="")

Jbrich95/sdfExtreme documentation built on March 24, 2022, 11:15 a.m.