exchEVTest {copula} | R Documentation |
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.
exchEVTest(x, N = 1000, estimator = "CFG", derivatives = "Cn", m = 100)
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
|
derivatives |
a string specifying how the derivatives of the
unknown copula are estimated; can be either |
m |
integer specifying the size of the integration grid for the statistic. |
More details are available in the first two references.
Returns a list whose attributes are:
statistic |
value of the test statistic. |
pvalue |
corresponding approximate p-value. |
This test was derived under the assumption of continuous margins, which implies that ties occur with probability zero. The presence of ties in the data might substantially affect the approximate p-value. One way of dealing with ties was suggested in the last reference.
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/.
## 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))