copula (version 0.999-15)

exchEVTest: Test of Exchangeability for Certain Bivariate Copulas

Description

Test for assessing the exchangeability of the underlying bivariate copula when it is either extreme-value or left-tail decreasing. The test uses the nonparametric estimators of the Pickands dependence function studied by Genest and Segers (2009).

The test statistic is defined in the second reference. An approximate p-value for the test statistic is obtained by means of a multiplier technique.

Usage

exchEVTest(x, N = 1000,  estimator = c("CFG", "Pickands"), derivatives = c("Cn", "An"), m = 100)

Arguments

x

a data matrix that will be transformed to pseudo-observations.

N

number of multiplier iterations to be used to simulate realizations of the test statistic under the null hypothesis.

estimator

string specifying which nonparametric estimator of the Pickands dependence function $A()$ to use; can be either "CFG" or "Pickands"; see Genest and Segers (2009).

derivatives

a string specifying how the derivatives of the unknown copula are estimated; can be either "An" or "Cn". The former should be used under the assumption of extreme-value dependence. The latter is faster; see the second reference.

m

integer specifying the size of the integration grid for the statistic.

Value

Returns a list whose attributes are:

Details

More details are available in the first two references.

References

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

Kojadinovic, I. and Yan, J. (2012) A nonparametric test of exchangeability for extreme-value and left-tail decreasing bivariate copulas. The Scandinavian Journal of Statistics. In press.

Kojadinovic, I. and Yan, J. (2010). Modeling Multivariate Distributions with Continuous Margins Using the copula R Package. Journal of Statistical Software 34(9), 1--20. http://www.jstatsoft.org/v34/i09/.

See Also

exchTest, gofCopula.

Examples

## Data from an exchangeable left-tail decreasing copulas
exchEVTest(rCopula(200,  gumbelCopula(3)))
exchEVTest(rCopula(200, claytonCopula(3)))

## An asymmetric Khoudraji-Gumbel-Hougaard copula
kc <- khoudrajiCopula(copula1 = indepCopula(),
                      copula2 = gumbelCopula(4),
                      shapes = c(0.4, 0.95))
exchEVTest(rCopula(200, kc))