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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)

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).

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.

Note

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.

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.

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.

copula

Multivariate Dependence with Copulas

v1.0-1

GPL (>= 3) | file LICENCE

Authors

Marius Hofert [aut] (<https://orcid.org/0000-0001-8009-4665>), Ivan Kojadinovic [aut] (<https://orcid.org/0000-0002-2903-1543>), Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Jun Yan [aut] (<https://orcid.org/0000-0003-4401-7296>), Johanna G. Nešlehová [ctb] (evTestK(), <https://orcid.org/0000-0001-9634-4796>), Rebecca Morger [ctb] (fitCopula.ml(): code for free mixCopula weight parameters)

Initial release

2020-12-07