copula (version 1.1-4)

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"))

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.

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.

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.

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))