exchEVTest {copula} | R Documentation

## 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 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, http://arxiv.org/abs/1609.05519.

### See Also

`exchTest`, `radSymTest`, `gofCopula`.

### 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))

[Package copula version 0.999-18 Index]