VineCopula (version 1.0)

BiCopGofKendall: Goodness-of-fit test based on Kendall's process for bivariate copula data

Description

This function performs the goodness-of-fit test based on Kendall's process for bivariate copula data. It computes the Cramer-von Mises and Kolmogorov-Smirnov test statistics, respectively, as well as the according p-values using bootstrapping.

Usage

BiCopGofKendall(u1, u2, family, B=100, level=0.05)

Arguments

u1,u2

Data vectors of equal length with values in [0,1].

family

An integer defining the bivariate copula family for which the test is performed: 1 = Gaussian copula 2 = Student t copula (t-copula) 3 = Clayton copula 4 = Gumbel copula 5 = Frank copul

B

Integer; number of bootstrap samples (default: B = 100). For B = 0 only the the test statistics are returned. WARNING: If B is chosen too large, computations will take very long.

level

Numeric; significance level of the goodness-of-fit test (default: level = 0.05).

Value

• p.value.CvM
  P-value of the goodness-of-fit test using the Cramer-von Mises statistic (if B > 0).
• p.value.KS
  P-value of the goodness-of-fit test using the Kolmogorov-Smirnov statistic (if B > 0).
• statistic.CvM
  The observed Cramer-von Mises test statistic.
• statistic.KS
  The observed Kolmogorov-Smirnov test statistic.

Details

This copula goodness-of-fit test is based on Kendall's process as investigated by Genest and Rivest (1993) and Wang and Wells (2000). For rotated copulas the input arguments are transformed and the goodness-of-fit procedure for the corresponding non-rotated copula is used.

References

Genest, C. and L.-P. Rivest (1993). Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association, 88 (423), 1034-1043. Luo J. (2011). Stepwise estimation of D-vines with arbitrary specified copula pairs and EDA Tools. Diploma thesis, Technische Universitaet Muenchen. http://mediatum.ub.tum.de/?id=1079291. Wang, W. and M. T. Wells (2000). Model selection and semiparametric inference for bivariate failure-time data. Journal of the American Statistical Association, 95 (449), 62-72.

See Also

BiCopIndTest, BiCopSelect, BiCopVuongClarke, BiCopKPlot, BiCopLambda

Examples

# sample from a Gaussian copula
par1 = 3
fam1 = 3
dat1 = BiCopSim(500,fam1,par1)

# perform the goodness-of-fit test for the true copula
gof = BiCopGofKendall(dat1[,1],dat1[,2],fam1)
gof$p.value.CvM
gof$p.value.KS

# perform the goodness-of-fit test for the Frank copula
gof = BiCopGofKendall(dat1[,1],dat1[,2],5)
gof$p.value.CvM
gof$p.value.KS