fExtDepSpat {ExtremalDep} | R Documentation |
Fitting of a max-stable process
Description
This function uses the Stephenson-Tawn likelihood to estimate parameters of max-stable models.
Usage
fExtDepSpat(model, z, sites, hit, jw, thresh, DoF, range, smooth,
alpha, par0, acov1, acov2, parallel, ncores, args1, args2,
seed=123, method = "BFGS", sandwich=TRUE,
control = list(trace=1, maxit=50, REPORT=1, reltol=0.0001))
Arguments
model |
A character string indicating the max-stable model, currently extremal-t ( |
z |
A |
sites |
A |
hit |
A |
jw |
An integer between |
thresh |
A positive real indicating the threshold value for pairwise distances. See |
DoF |
A positive real indicating a fixed value of the degree of freedom of the extremal-t and extremal skew-t models. |
range |
A positive real indicating a fixed value of the range parameter for the power exponential correlation function (only correlation function currently available). |
smooth |
A positive real in |
alpha |
A vector of length |
par0 |
A vector of initial value of the parameter vector, in order the degree of freedom |
acov1 , acov2 |
Vectors of length |
parallel |
A logical value; if |
ncores |
An integer indicating the number of cores considered in the parallel socket cluster of type |
args1 , args2 |
Lists specifying details about the Monte Carlo simulation schereme to compute multivariate CDFs. See |
seed |
An integer for reproduciblity in the CDF computations. |
method |
A character string indicating the optimisation method to be used. See |
sandwich |
A logical value; if |
control |
A list of control parameter for the optimisation. See |
Details
This routine follows the methodology developped by Beranger et al. (2021). It uses on the Stephenson-Tawn which relies on the knowledge of time occurrences of each block maxima. Rather than considering all partitions of the set , the likelihood is computed using the observed partition. Let
denote the observed partition, then the Stephenson-Tawn likelihood is given by
where represents the partial derivative(s) of
with respect to
.
When jw=d
the full Stephenson-Tawn likelihood is considered whereas for values lower than a composite likelihood approach is taken.
The argument thresh
is required when the composite likelihood is used. A tuple of size jw
, is assigned a weight of one if the maximum pairwise distance between corresponding locations is less that thresh
and a weight of zero otherwise.
Arguments args1
and args2
relate to specifications of the Monte Carlo simulation scheme to compute multivariate CDF evaluations. These should take the form of lists including the minimum and maximum number of simulations used (Nmin
and Nmax
), the absolute error (eps
) and whether the error should be controlled on the log-scale (logeps
).
Value
A list comprising of the vector of estimated parameters (est
), the composite likelihood order (jw
), the maximised log-likelihood value (LL
). In addition, if sandwich=TRUE
the the standard errors from the sandwich information matrix are reported via stderr.sand
as well as the TIC for model selection (TIC
). Finally, if the composite likelihood is considered, a matrix with all tuples considered with a weight of 1 are reported in cmat
.
Author(s)
Simone Padoan, simone.padoan@unibocconi.it, https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, borisberanger@gmail.com https://www.borisberanger.com;
References
Beranger, B., Stephenson, A. G. and Sisson, S.A. (2021) High-dimensional inference using the extremal skew-t process Extremes, 24, 653-685.
See Also
Examples
set.seed(14342)
# Simulation of 20 locations
Ns <- 20
sites <- matrix(runif(Ns*2)*10-5,nrow=Ns,ncol=2)
for(i in 1:2) sites[,i] <- sites[,i] - mean(sites[,i])
# Simulation of 50 replicates from the Extremal-t model
Ny <- 50
z <- rExtDepSpat(Ny, sites, model="ET", cov.mod="powexp", DoF=1,
range=3, nugget=0, smooth=1.5,
control=list(method="exact"))
# Fit the extremal-t using the full Stephenson-Tawn likelihood
args1 <- list(Nmax=50L, Nmin=5L, eps=0.001, logeps=FALSE)
args2 <- list(Nmax=500L, Nmin=50L, eps=0.001, logeps=TRUE)
## Not run:
fit1 <- fExtDepSpat(model="ET", z=z$vals, sites=sites, hit=z$hits,
par0=c(3,1,1), parallel=TRUE, ncores=6,
args1=args1, args2=args2, control = list(trace=0))
fit1$est
## End(Not run)