copula (version 1.1-4)

evTestA: Bivariate Test of Extreme-Value Dependence Based on Pickands' Dependence Function

Description

Test of bivariate extreme-value dependence based on the process comparing the empirical copula with a natural nonparametric estimator of the unknown copula derived under extreme-value dependence. The test statistics are defined in the third reference. Approximate p-values for the test statistics are obtained by means of a multiplier technique.

Usage

evTestA(x, N = 1000, derivatives = c("An","Cn"),
        ties.method = eval(formals(rank)$ties.method),
        trace.lev = 0, report.err = FALSE)

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 approximate p-value.

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.

derivatives

string specifying how the derivatives of the unknown copula are estimated, either "An" or "Cn". The former gives better results for samples smaller than 400 but is slower.

ties.method

character string specifying how ranks should be computed if there are ties in any of the coordinate samples of x; passed to pobs.

trace.lev

integer indicating the level of diagnostic tracing to be printed to the console (from low-level algorithm).

report.err

logical indicating if numerical integration errors should be reported in a summary way.

Details

More details are available in the third reference. See also Genest and Segers (2009) and Remillard and Scaillet (2009).

References

Genest, C. and Segers, J. (2009). Rank-based inference for bivariate extreme-value copulas. Annals of Statistics, 37, pages 2990-3022.

Rémillard, B. and Scaillet, O. (2009). Testing for equality between two copulas. Journal of Multivariate Analysis, 100(3), pages 377-386.

Kojadinovic, I. and Yan, J. (2010). Nonparametric rank-based tests of bivariate extreme-value dependence. Journal of Multivariate Analysis 101, 2234--2249.

See Also

evTestK, evTestC, evCopula, gofEVCopula, An.

Examples

## Do these data come from an extreme-value copula?
set.seed(63)
uG <- rCopula(100, gumbelCopula (3))
uC <- rCopula(100, claytonCopula(3))
## these two take 21 sec on nb-mm4 (Intel Core i7-5600U @ 2.60GHz):
evTestA(uG)
evTestA(uC) # significant even though Clayton is *NOT* an extreme value copula

## These are fast:
evTestA(uG, derivatives = "Cn")
evTestA(uC, derivatives = "Cn") # small p-value even though Clayton is *NOT* an EV copula.


set.seed(34)
tG   <- evTestA(uG[1:10,])
tC.A <- evTestA(uC[1:12,])
tC.C <- evTestA(uC[1:20,], derivatives = "Cn")
stopifnot(
 all.equal(tG  $p.value, 27/2002,  tolerance= 1e-15),
 all.equal(tC.C$p.value,   1/182 , tolerance= 1e-15),
 all.equal(tC.C$p.value, tC.A$p.value, tolerance = 1e-15) # in < 10% of cases
)