exchTest {copula} | R Documentation |
Test for assessing the exchangeability of the underlying bivariate copula based on the empirical copula. The test statistics are defined in the first two references. Approximate p-values for the test statistics are obtained by means of a multiplier technique.
exchTest(x, N = 1000, m = 0)
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. |
m |
if |
More details are available in the two first references.
Returns a list whose attributes are:
statistic |
value of the test statistic. |
p.value |
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., G. Nešlehová, J. and Quessy, J.-F. (2012). Tests of symmetry for bivariate copulas. Annals of the Institute of Statistical Mathematics. In press.
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), pages 1-20.
## Do these data come from exchangeable copulas? exchTest(rCopula(200, gumbelCopula(3))) exchTest(rCopula(200, claytonCopula(3))) ## Creating asymmetric data khoudraji <- function(cop,n,a=0.6,b=0.95) { u <- rCopula(n, cop) 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 } exchTest(khoudraji(gumbelCopula(3),200)) exchTest(khoudraji(claytonCopula(3),200))