copula (version 0.999-7)

evTestK: Bivariate Test of Extreme-Value Dependence Based on Kendall's Process

Description

Test of extreme-value dependence based on the bivariate probability integral transformation. The test statistic is defined in Ben Ghorbal, G. Nešlehová{Neslehova}, and Genest (2009).

Usage

evTestK(x, method = c("fsample","asymptotic","jackknife"))

Arguments

x

a data matrix.

method

specifies the variance estimation method; can be either "fsample" (finite-sample, the default), "asymptotic" or "jackknife".

Value

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

Details

The code for this test was generously provided by Johanna G. Nešlehová{Neslehova}. More details are available in Appendix B of Ben Ghorbal, G. Nešlehová{Neslehova} and Genest (2009).

References

Ghorbal, M. B., Genest, C., and G. Nešlehová{Neslehova}, J. (2009) On the test of Ghoudi, Khoudraji, and Rivest for extreme-value dependence. The Canadian Journal of Statistics 37, 1--9.

See Also

evTestC, evTestA, evCopula, gofEVCopula, An.

Examples

set.seed(321)
## Do the data come from an extreme-value copula?
evTestK(Ug <- rCopula(200, gumbelCopula(3))) # not significant => yes, EV
    dim(Uc <- rCopula(200, claytonCopula(3)))
## Clayton:                       tests are highly significant => no, not EV
(K1 <- evTestK(Uc))
(K2 <- evTestK(Uc, method = "asymptotic"))
(K3 <- evTestK(Uc, method = "jackknife"))# slow !
Xtra <- copula:::doExtras()
stopifnot(all.equal(K1$p.value, 3.9471315e-9, tol = .001),
          all.equal(K2$p.value, 2.1277296e-9, tol = .001),
          if(Xtra) { set.seed(1)
            print(system.time(K3 <- evTestK(Uc, method = "jackknife")))
            all.equal(K3$p.value, 0.0 , tol = .001) # ??
          } else TRUE
         )
system.time(T1 <- evTestK(Ug))
system.time(T2 <- evTestK(Ug, method = "asymptotic"))
stopifnot(all.equal(T1$p.value, 0.1363025, tol = .001),
          all.equal(T2$p.value, 0.1217252, tol = .001),
          if(Xtra) { set.seed(2)
            print(system.time(T3 <- evTestK(Ug, method = "jackknife")))# 3.6 sec
            all.equal(T3$p.value, 0.0 , tol = .001) #?
          } else TRUE
         )