exchEVTest: Test of exchangeability for extreme-value and left-tail decreasing 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 = "CFG", derivatives = "Cn", m = 100)

Arguments

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

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

estimator

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

derivatives

specifies 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 referenc

specifies the size of the integration grid for the statistic.

Value

Returns a list whose attributes are:
statisticvalue of the test statistic.
pvaluecorresponding approximate p-value.

Details

More details are available in the two first references.

References

C. Genest and J. Segers (2009). Rank-based inference for bivariate extreme-value copulas. Annals of Statistics, 37, pages 2990-3022. I. Kojadinovic and J. Yan (2012). A nonparametric test of exchangeability for extreme-value and left-tail decreasing bivariate copulas. The Scandinavian Journal of Statistics. In press.

I. Kojadinovic and J. Yan (2010). Modeling Multivariate Distributions with Continuous Margins Using the copula R Package. Journal of Statistical Software, 34(9), pages 1-20.

Examples

Run this code

## Do these data come from exchangeable copulas? 
exchEVTest(rcopula(gumbelCopula(3), 200)) 
exchEVTest(rcopula(claytonCopula(3), 200))

## Creating asymmetric data 
khoudraji <- function(cop,n,a=0.6,b=0.95)
  {
    u <- rcopula(cop,n)
    v <- matrix(runif(2*n),n,2)
    x <- cbind(pmax(u[,1]^(1/a),v[,1]^(1/(1-a))),
               pmax(u[,2]^(1/b),v[,2]^(1/(1-b))))
    x
  }
exchEVTest(khoudraji(gumbelCopula(3),200))
exchEVTest(khoudraji(claytonCopula(3),200))

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