copula (version 0.99-4)

evTestA: Bivariate test of extreme-value dependence based on the 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 = "An")

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

specifies how the derivatives of the unknown copula are estimated; can be either "An" or "Cn". The former gives better results for samples smaller than 400 but is slower.

Value

• Returns a list whose attributes are:
• statistic
  value of the test statistic.
• pvalue
  corresponding approximate p-value.

Details

More details are available in the third reference. See also Genest and Segers (2009) and Remillard and Scaillet (2009).

References

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

B. Remillard and O. Scaillet (2009). Testing for equality between two copulas. Journal of Multivariate Analysis, 100(3), pages 377-386.

I. Kojadinovic and J. Yan (2010). Nonparametric rank-based tests of bivariate extreme-value dependence. Journal of Multivariate Analysis 101, 2234--2249.

I. Kojadinovic and J. Yan (2010). Modeling Multivariate Distributions with Continuous Margins Using the copula R Package. Journal of Statistical Software, 34(9), pages 1-20.

See Also

evTestK, evTestC, evCopula, gofEVCopula, Anfun.

Examples

## Do these data come from an extreme-value copula?
uG <- rcopula(gumbelCopula(3), 100)
uC <- rcopula(claytonCopula(3), 100)
evTestA(uG)
evTestA(uG, derivatives = "Cn")

evTestA(uC)
evTestA(uG[1:10,])
evTestA(uG[1:10,], derivatives = "Cn")