maxlik: Maximum likelihood estimation
In HiDimMaxStable: Inference on High Dimensional Max-Stable Distributions

Description Usage Arguments Value See Also Examples

The maxlik.* function family computes the maximum likelihood from data of a max-stable distribution or in the maximum domain of attraction of a max-stable distribution. * must be one of the following: "maxstable", "excess" or "simultoccur".

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maxlik.maxstable(...)
maxlik.excess(...)
maxlik.simultoccur(...)

...

all the arguments to be passed to the likelihood function including:

data: a matrix representing the data
params: a vector giving the arguments to be passed to the likelihood function. NA indicates the coordinates that will be used for the optimization of the likelihood function.
start: a vector giving the initial values of the parameters
trace: when TRUE, prints the values where the likelihood function is evaluated
iterlim: the maximum number of iterations

returns a list l including the following components: l$estimate giving the estimated parameter values, l$message giving a short message describing if the convergence is successfull, l$iterations giving the number of iterations...

maxLik, maxstable.l.clusters, excess.l, simultoccur.l.

# ML estimation for a sample from a Schlather max-stable distribution
# (Use larger values for n.site and n.obs to get good results!)
n.site<-2
n.obs<-2
xy<-matrix(runif(2 * n.site, 0, 0.5), ncol = 2)
param<-c(0.5,1.5)
library(SpatialExtremes)
data<-t(rmaxstab(n.obs, xy, "whitmat",
                 nugget = 0, range = param[1], smooth = param[2]))
ml<-maxlik.maxstable(data,params=c(NA,NA),start=c(1,1),
                      category="normal",
                      spatial=list(sites=xy,family=spatialWhittleMatern),
                      iterlim=4)


# ML estimation for a sample in the max domain of attraction
# of from an homogeneous clustered max-stable distribution
#
# WARNING: these exemples are quite time-consuming, but yet need
# larger values for n and the dimensions for correct results

# A) using excess

raw.data<-rCMS(copulas=c(copClayton,copGumbel),
               margins=c(marginLnorm,marginFrechet),
               classes=c(rep(1,3),rep(2,3)),
               params=c(0.5,1,1.5,1.7),n=20)
data<-excess.censor(raw.data)
d<-dens.grid.excess(data,c(NA,1,NA,1.7),
                    seq(0.1,1,length=5),seq(1,2,length=5),
                    category="copula",
                    copulas=c(copClayton,copGumbel),
                    margins=c(marginLnorm,marginFrechet),
                    classes=c(rep(1,3),rep(2,3)))
plot3d.densgrid(d)
ml<-maxlik.excess(data,
                  params=c(NA,NA,NA,NA),start=c(0.5,1,1.5,1.7),
                  trace=TRUE,iterlim=20,
                  category="copula",
                  copulas=c(copClayton,copGumbel),
                  margins=c(marginLnorm,marginFrechet),
                  classes=c(rep(1,3),rep(2,3)))

# B) using block maxima with occurences

raw.data<-rCMS(copulas=c(copClayton,copGumbel),
               margins=c(marginLnorm,marginFrechet),
               classes=c(rep(1,3),rep(2,3)),
               params=c(0.5,1,1.5,1.7),n=10)
data<-maxblocks(raw.data,n.blocks=2)
d<-dens.grid.simultoccur(data$normalized.max,occur=data$classes.max,
                         c(NA,1,NA,1.7),
                         seq(0.1,1,length=5),seq(1,2,length=5),
                         category="copula",
                         copulas=c(copClayton,copGumbel),
                         margins=c(marginLnorm,marginFrechet),
                         classes=c(rep(1,3),rep(2,3)))
plot3d.densgrid(d)
ml<-maxlik.simultoccur(data$normalized.max,
                       params=c(NA,NA,NA,NA),start=c(0.5,1,1.5,1.7),
                       trace=TRUE,iterlim=20,
                       occur=data$classes.max,
                       category="copula",
                       copulas=c(copClayton,copGumbel),
                       margins=c(marginLnorm,marginFrechet),
                       classes=c(rep(1,3),rep(2,3)))