copula (version 0.999-1)

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.
• p.value
  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

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

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

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

Kojadinovic, I. and Yan, J. (2010). Modeling Multivariate Distributions with Continuous Margins Using the copula R Package. Journal of Statistical Software 34(9), 1--20. http://www.jstatsoft.org/v34/i09/.

See Also

evTestK, evTestC, evCopula, gofEVCopula, An.

Examples

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

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