copula (version 0.999-7)

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 = "CFG", derivatives = "Cn", 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 secon

m

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

Value

• Returns a list whose attributes are:
• statistic
  value of the test statistic.
• pvalue
  corresponding approximate p-value.

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

## Do these data come from exchangeable copulas?
exchEVTest(rCopula(200,  gumbelCopula(3)))
exchEVTest(rCopula(200, claytonCopula(3)))## Creating asymmetric data
rKhoudraji <- function(cop,n,a=0.6,b=0.95)
  {
    u <- rCopula(n, cop)
    v <- matrix(runif(2*n),n,2)
    cbind(pmax(u[,1]^(1/a),v[,1]^(1/(1-a))),
          pmax(u[,2]^(1/b),v[,2]^(1/(1-b))))
  }
exchEVTest(rKhoudraji( gumbelCopula(3),200))
exchEVTest(rKhoudraji(claytonCopula(3),200))