fitFDG(FDGcopula, data, depcoefType="spearman", nbInit=1, W=NA, method="L-BFGS-B", estimate.variance=TRUE, nb.rep=100, nb.obs=100, dcData=NA, sizeSubSample=10000)
fitFDG
class object containing the slots:
dcData
. The estimation of the asymptotic
variance-covariance matrix of 'sqrt(n)(theta hat - theta)', where 'n' is
the sample size, 'theta' is the parameter vector, and 'theta hat' is the
weighted least square estimator, is carried out by simulation. More
precisely, nb.rep
replications of datasets of size nb.obs
are
simulated according to the fitted FDG copula. For each dataset,
the sample dependence coefficients are calculated, and, then, their sample variances / covariances are computed. In the case where the upper tail
dependence coefficients were chosen to perform the estimation, a
different approximation is used. Since the
margins are assumed to be known, there is a simple formula
for the variances / covariances given in (15) of [2]. These quantities
within this formula can be approximated by standard empirical means
calculated on a single big dataset from the underlying extreme-value
copula. To simulate that dataset, the variable sizeSubSample
is used
along with nb.rep
: nb.rep
sub-samples of size sizeSubSample
are
simulated, and for each sub-sample, the maximum is taken, thus leading
to a final dataset of size nb.rep
. The empirical means to
approximate the asymptotic variances / covariances are computed on
this last final dataset.
fitFDG-class
## Create an object of class 'FDGcopula'
theta <- c(.3,.5,.7,.9)
myFDGcopula <- FDGcopula("frechet", theta)
## Generate a sample from a FDG copula with Frechet generators
## and parameter vector 'theta'
dat <- rFDG(100, myFDGcopula)
## Fit a FDG copula to the data
myFittedCopula <- fitFDG(myFDGcopula, dat)
myFittedCopula
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