BiCopGofKendall: Goodness-of-fit test based on Kendall's process for bivariate...
In CDVine: Statistical Inference of C- And D-Vine Copulas

Description Usage Arguments Details Value Author(s) References See Also Examples

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.

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

`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`).

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.

`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.

Jiying Luo, Eike Brechmann

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.

BiCopIndTest, BiCopSelect, BiCopVuongClarke, BiCopKPlot, BiCopLambda

# 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)

The CDVine package is no longer developed actively.
Please consider using the more general VineCopula package
(see https://CRAN.R-project.org/package=VineCopula),
which extends and improves the functionality of CDVine.

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