CDVine (version 1.4)

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 copula 6 = Joe copula 7 = BB1 copula 8 = BB6 copula 9 = BB7 copula 10 = BB8 copula 13 = rotated Clayton copula (180 degrees; ``survival Clayton'') 14 = rotated Gumbel copula (180 degrees; ``survival Gumbel'') 16 = rotated Joe copula (180 degrees; ``survival Joe'') 17 = rotated BB1 copula (180 degrees; ``survival BB1'') 18 = rotated BB6 copula (180 degrees; ``survival BB6'') 19 = rotated BB7 copula (180 degrees; ``survival BB7'') 20 = rotated BB8 copula (180 degrees; ``survival BB8'') 23 = rotated Clayton copula (90 degrees) 24 = rotated Gumbel copula (90 degrees) 26 = rotated Joe copula (90 degrees) 27 = rotated BB1 copula (90 degrees) 28 = rotated BB6 copula (90 degrees) 29 = rotated BB7 copula (90 degrees) 30 = rotated BB8 copula (90 degrees) 33 = rotated Clayton copula (270 degrees) 34 = rotated Gumbel copula (270 degrees) 36 = rotated Joe copula (270 degrees) 37 = rotated BB1 copula (270 degrees) 38 = rotated BB6 copula (270 degrees) 39 = rotated BB7 copula (270 degrees) 40 = rotated BB8 copula (270 degrees)

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/doc/1079291/1079291.pdf.

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)

## Not run: 
# # 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
# ## End(Not run)