gnacopula {copula} | R Documentation |
Goodness-of-fit Testing for (Nested) Archimedean Copulas
Description
gnacopula()
conducts a goodness-of-fit test for the given
(H_0
-)copula cop
based on the (copula-)data u
.
NOTE: gnacopula()
is deprecated, call gofCopula()
instead.
Usage
gnacopula(u, cop, n.bootstrap,
estim.method = eval(formals(enacopula)$method),
include.K=TRUE, n.MC=0, trafo=c("Hering.Hofert", "Rosenblatt"),
method=eval(formals(gofTstat)$method), verbose=TRUE, ...)
Arguments
u |
|
cop |
|
n.bootstrap |
positive integer specifying the number of bootstrap replicates. |
estim.method |
|
include.K |
logical indicating whether the last component, involving the
Kendall distribution function |
n.MC |
parameter |
trafo |
a |
method |
a |
verbose |
if |
... |
additional arguments passed to |
Details
The function gnacopula()
performs a parametric bootstrap for the
goodness-of-fit test specified by trafo
and method
. The
transformation given by trafo
specifies the multivariate
transformation which is first applied to the (copula-) data u
(typically, the pseudo-observations are used); see
htrafo()
or cCopula()
for more details. The
argument method
specifies the particular goodness-of-fit test
carried out, which is either the Anderson-Darling test for the
univariate standard uniform distribution (for method="AnChisq"
or
method="AnGamma"
) in a one-dimensional setup or the tests
described in Genest et al. (2009) for the
multivariate standard uniform distribution directly in a multivariate
setup. As estimation method, the method provided by
estim.method
is used.
Note that a finite-sample correction is made when computing p-values;
see gofCopula()
for details.
A word of warning: Do work carefully with the variety of different
goodness-of-fit tests that can be performed with gnacopula()
.
For example, among the possible estimation methods at hand, only
MLE is known to be consistent (under conditions to be verified).
Furthermore, for the tests based on the Anderson-Darling test
statistic, it is theoretically not clear whether the parametric bootstrap
converges. Consequently, the results obtained should be treated with
care. Moreover, several estimation methods are known to be prone to
numerical errors (see Hofert et al. (2013)) and are thus not
recommended to be used in the parametric bootstrap. A warning is given if
gnacopula()
is called with a method not being MLE.
Value
gnacopula
returns an R object of class "htest"
.
This object contains a list with the bootstrap results including the
components
p.value
:the bootstrapped p-value;
statistic
:the value of the test statistic computed for the data
u
;data.name
:the name of
u
;method
:a
character
describing the goodness-of-fit test applied;estimator
:the estimator computed for the data
u
;bootStats
:a list with component
estimator
containing the estimators for all bootstrap replications and componentstatistic
containing the values of the test statistic for each bootstrap replication.
References
Genest, C., Rémillard, B., and Beaudoin, D. (2009), Goodness-of-fit tests for copulas: A review and a power study Insurance: Mathematics and Economics 44, 199–213.
Rosenblatt, M. (1952), Remarks on a Multivariate Transformation, The Annals of Mathematical Statistics 23, 3, 470–472.
Hering, C. and Hofert, M. (2011), Goodness-of-fit tests for Archimedean copulas in large dimensions, submitted.
Hofert, M., Mächler, M., and McNeil, A. J. (2012). Likelihood inference for Archimedean copulas in high dimensions under known margins. Journal of Multivariate Analysis 110, 133–150.
See Also
gofTstat()
for the implemented test statistis,
htrafo()
and cCopula()
involved and
K()
for the Kendall distribution function.
gofCopula()
for other (parametric bootstrap) based
goodness-of-fit tests.