copula (version 0.99-4)

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, Nešlehová and Yan (2010). Approximate p-values for the test statistic are obtained using a parametric bootstrap.

Usage

gofEVCopula(copula, x, N = 1000, method = "mpl",
            estimator = "CFG", m = 1000, print.every = 100,
            optim.method = "Nelder-Mead")

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.

print.every

progress is printed every "print.every" iterations. No progress is printed if it is nonpositive.

optim.method

the method for "optim".

Value

• Returns a list whose attributes are:
• statistic
  value of the test statistic.
• pvalue
  corresponding approximate p-value.
• parameters
  estimates of the parameters for the hypothesized copula family.

encoding

UTF-8

Details

More details can be found in the second reference.

References

C. Genest and J. Segers (2009). Rank-based inference for bivariate extreme-value copulas. Annals of Statistics, 37, pages 2990-3022.

C. Genest, I. Kojadinovic, J. Nešlehová and J. Yan (2011). A goodness-of-fit test for bivariate extreme-value copulas. Bernoulli 17, 1, pages 253-275.

See Also

evCopula, evTestC, evTestA, evTestK, gofCopula, Anfun.

Examples

x <- rcopula(claytonCopula(3), 100)

## Does the Gumbel family seem to be a good choice?
gofEVCopula(gumbelCopula(1), x)

## The same with different estimation methods
gofEVCopula(gumbelCopula(1), x, method="itau")
gofEVCopula(gumbelCopula(1), x, method="irho")

## The same with different extreme-value copulas
gofEVCopula(galambosCopula(1), x)
gofEVCopula(galambosCopula(1), x, method="itau")
gofEVCopula(galambosCopula(1), x, method="irho")
gofEVCopula(huslerReissCopula(1), x)
gofEVCopula(huslerReissCopula(1), x, method="itau")
gofEVCopula(huslerReissCopula(1), x, method="irho")
gofEVCopula(tevCopula(0, df.fixed=TRUE), x)
gofEVCopula(tevCopula(0, df.fixed=TRUE), x, method="itau")
gofEVCopula(tevCopula(0, df.fixed=TRUE), x, method="irho")