copula (version 1.1-4)

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

Description

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

Usage

evTestK(x, method = c("fsample","asymptotic","jackknife"), ties = NA, N = 100)

Value

An object of class

htest which is a list, some of the components of which are

statistic

value of the test statistic.

p.value

corresponding p-value.

Arguments

x

a data matrix.

method

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

ties

logical; if TRUE, the original test is adapted to take the presence of ties in the coordinate samples of x into account; the default value of NA indicates that the presence/absence of ties will be checked for automatically.

N

number of samples to be used to estimate a bias term if ties = TRUE.

Details

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

References

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

Kojadinovic, I. (2017). Some copula inference procedures adapted to the presence of ties. Computational Statistics and Data Analysis 112, 24--41, https://arxiv.org/abs/1609.05519.

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"))
# \donttest{
system.time(print(K3 <- evTestK(Uc, method = "jackknife")))
## slower: 1.06 sec (2015 intel core i7)
# }
# \dontshow{
Xtra <- copula:::doExtras()
stopifnot(all.equal(K1$p.value, 3.9471315e-9, tolerance = .001),
          all.equal(K2$p.value, 2.1277296e-9, tolerance = .001),
          if(Xtra) { set.seed(1)
            print(system.time(K3 <- evTestK(Uc, method = "jackknife")))
            all.equal(K3$p.value, 0.0 , tolerance = .001) # ??
          } else TRUE
         )
system.time(T1 <- evTestK(Ug))
system.time(T2 <- evTestK(Ug, method = "asymptotic"))
stopifnot(all.equal(T1$p.value, 0.1363025, tolerance = .001),
          all.equal(T2$p.value, 0.1217252, tolerance = .001),
          if(Xtra) { set.seed(2)
            print(system.time(T3 <- evTestK(Ug, method = "jackknife")))# 3.6 sec
            all.equal(T3$p.value, 0.1507736 , tolerance = .001) #?
          } else TRUE
         )
# }