copula (version 0.999-15)

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(), optim.method = "BFGS")

Arguments

copula

object of class "evCopula" representing the hypothesized extreme-value copula family.

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 "mpl" (maximum pseudo-likelihood), "itau" (inversion of Kendall's tau) or "irho" (inversion of Spearman's rho).

estimator

specifies which nonparametric rank-based estimator of the unknown Pickands dependence function to use; can be either "CFG" (Caperaa-Fougeres-Genest) or "Pickands".

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 txtProgressBar.

optim.method

a string, the method for optim(). In copula versions 0.999-14 and earlier, the default was "Nelder-Mead", but now is set to the same as for fitCopula().

Value

An object of class htest which is a list, some of the components of which are

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 # (for now)
x <- rCopula(n, claytonCopula(3))


## Does the Gumbel family seem to be a good choice?
gofEVCopula(gumbelCopula(), x)


## 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)
gofEVCopula(galambosCopula(), x, method="itau")
gofEVCopula(galambosCopula(), x, method="irho")

gofEVCopula(huslerReissCopula(), x)
gofEVCopula(huslerReissCopula(), x, method="itau")
gofEVCopula(huslerReissCopula(), x, method="irho")

gofEVCopula(tevCopula(df.fixed=TRUE), x)
gofEVCopula(tevCopula(df.fixed=TRUE), x, method="itau")
gofEVCopula(tevCopula(df.fixed=TRUE), x, method="irho")