copula: exchEVTest – R documentation

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exchEVTest

Test of Exchangeability for Certain Bivariate Copulas

Description

Test for assessing the exchangeability of the underlying bivariate copula when it is either extreme-value or left-tail decreasing. The test uses the nonparametric estimators of the Pickands dependence function studied by Genest and Segers (2009).

The test statistic is defined in the second reference. An approximate p-value for the test statistic is obtained by means of a multiplier technique if there are no ties in the component series of the bivariate data, or by means of an appropriate bootstrap otherwise.

Usage

exchEVTest(x, N = 1000,  estimator = c("CFG", "Pickands"),
           ties = NA, ties.method = eval(formals(rank)$ties.method),
           m = 100, derivatives = c("Cn", "An"))

Arguments

`x`	a data matrix that will be transformed to pseudo-observations.
`N`	number of multiplier or boostrap iterations to be used to simulate realizations of the test statistic under the null hypothesis.
`estimator`	string specifying which nonparametric estimator of the Pickands dependence function A() to use; can be either `"CFG"` or `"Pickands"`; see Genest and Segers (2009).
`ties`	logical; if `FALSE`, approximate p-values are computed by means of a multiplier bootstrap; if `TRUE`, a boostrap adapted to the presence of ties in any of the coordinate samples of `x` is used; the default value of `NA` indicates that the presence/absence of ties will be checked for automatically.
`ties.method`	string specifying how ranks should be computed if there are ties in any of the coordinate samples of `x`; passed to `pobs`.
`derivatives`	a string specifying how the derivatives of the unknown copula are estimated; can be either `"An"` or `"Cn"`. The former should be used under the assumption of extreme-value dependence. The latter is faster; see the second reference.
`m`	integer specifying the size of the integration grid for the statistic.

Details

More details are available in the references.

Value

An object of class htest which is a list, some of the components of which are

`statistic`	value of the test statistic.
`pvalue`	corresponding approximate p-value.

References

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

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 39:3, 480–496.

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.

Examples

## Data from an exchangeable left-tail decreasing copulas
exchEVTest(rCopula(200,  gumbelCopula(3)))
exchEVTest(rCopula(200, claytonCopula(3)))

## An asymmetric Khoudraji-Gumbel-Hougaard copula
kc <- khoudrajiCopula(copula1 = indepCopula(),
                      copula2 = gumbelCopula(4),
                      shapes = c(0.4, 0.95))
exchEVTest(rCopula(200, kc))

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