copula (version 1.1-7)

gofEVCopula: 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), ...)

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.

Details

More details can be found in the second reference.

The former argument print.every is deprecated and not supported anymore; use verbose instead.

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")