gofEVCopula {copula} | R Documentation |
Goodness-of-fit Tests for Bivariate Extreme-Value Copulas
Description
Goodness-of-fit tests for extreme-value copulas based on the empirical process comparing one of the two nonparameteric rank-based estimator of the Pickands dependence function studied in Genest and Segers (2009) with a parametric estimate of the Pickands dependence function derived under the null hypothesis. The test statistic is the Cramer-von Mises functional Sn defined in Equation (5) of Genest, Kojadinovic, G. Nešlehová, and Yan (2010). Approximate p-values for the test statistic are obtained using a parametric bootstrap.
Usage
gofEVCopula(copula, x, N = 1000,
method = c("mpl", "ml", "itau", "irho"),
estimator = c("CFG", "Pickands"), m = 1000,
verbose = interactive(),
ties.method = c("max", "average", "first", "last", "random", "min"),
fit.ties.meth = eval(formals(rank)$ties.method), ...)
Arguments
copula |
object of class |
x |
a data matrix that will be transformed to pseudo-observations. |
N |
number of bootstrap samples to be used to simulate realizations of the test statistic under the null hypothesis. |
method |
estimation method to be used to estimate the
dependence parameter(s); can be either |
estimator |
specifies which nonparametric rank-based estimator
of the unknown Pickands dependence function to use; can be either
|
m |
number of points of the uniform grid on [0,1] used to compute the test statistic numerically. |
verbose |
a logical specifying if progress of the bootstrap
should be displayed via |
ties.method |
string specifying how ranks should be computed,
except for fitting, if there are ties in any of the coordinate
samples of |
fit.ties.meth |
string specifying how ranks should be computed
when fitting by maximum pseudo-likelihood if there are ties in any
of the coordinate samples of |
... |
further optional arguments, passed to
|
Details
More details can be found in the second reference.
The former argument print.every
is deprecated and not
supported anymore; use verbose
instead.
Value
An object of class
htest
which is a list,
some of the components of which are
statistic |
value of the test statistic. |
p.value |
corresponding approximate p-value. |
parameter |
estimates of the parameters for the hypothesized copula family. |
Note
For a given degree of dependence, the most popular bivariate extreme-value copulas are strikingly similar.
References
Genest, C. and Segers, J. (2009). Rank-based inference for bivariate extreme-value copulas. Annals of Statistics 37, 2990–3022.
Genest, C. Kojadinovic, I., G. Nešlehová, J., and Yan, J. (2011). A goodness-of-fit test for bivariate extreme-value copulas. Bernoulli 17(1), 253–275.
See Also
evCopula
, evTestC
, evTestA
,
evTestK
, gofCopula
, An
.
Examples
n <- 100; N <- 1000 # realistic (but too large currently for CRAN checks)
n <- 60; N <- 200 # (time (and tree !) saving ...)
x <- rCopula(n, claytonCopula(3))
## Does the Gumbel family seem to be a good choice?
gofEVCopula(gumbelCopula(), x, N=N)
## The same with different (and cheaper) estimation methods:
gofEVCopula(gumbelCopula(), x, N=N, method="itau")
gofEVCopula(gumbelCopula(), x, N=N, method="irho")
## The same with different extreme-value copulas
gofEVCopula(galambosCopula(), x, N=N)
gofEVCopula(galambosCopula(), x, N=N, method="itau")
gofEVCopula(galambosCopula(), x, N=N, method="irho")
gofEVCopula(huslerReissCopula(), x, N=N)
gofEVCopula(huslerReissCopula(), x, N=N, method="itau")
gofEVCopula(huslerReissCopula(), x, N=N, method="irho")
gofEVCopula(tevCopula(df.fixed=TRUE), x, N=N)
gofEVCopula(tevCopula(df.fixed=TRUE), x, N=N, method="itau")
gofEVCopula(tevCopula(df.fixed=TRUE), x, N=N, method="irho")