exchEVTest | R Documentation |
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.
exchEVTest(x, N = 1000, estimator = c("CFG", "Pickands"),
ties = NA, ties.method = eval(formals(rank)$ties.method),
m = 100, derivatives = c("Cn", "An"))
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 |
ties |
logical; if |
ties.method |
string specifying how ranks should be computed if
there are ties in any of the coordinate samples of |
derivatives |
a string specifying how the derivatives of the
unknown copula are estimated; can be either |
m |
integer specifying the size of the integration grid for the statistic. |
More details are available in the references.
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. |
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.
exchTest
, radSymTest
, gofCopula
.
## 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))
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