BiCopIndTest: Independence test for bivariate copula data

In CDVine: Statistical Inference of C- And D-Vine Copulas

Description

This function returns the p-value of a bivariate asymptotic independence test based on Kendall's tau.

Usage

BiCopIndTest(u1, u2)

Arguments

u1,u2

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

Details

The test exploits the asymptotic normality of the test statistic

statistic := T = ( (9N(N-1)) / (2(2N+5)) )^0.5 * |τ|,

where N is the number of observations (length of u1) and \hat{τ} the empirical Kendall's tau of the data vectors u1 and u2. The p-value of the null hypothesis of bivariate independence hence is asymptotically

p.value = 2*(1-Φ(T)),

where Φ is the standard normal distribution function.

Value

statistic	Test statistic of the independence test.
p.value	P-value of the independence test.

Author(s)

Jeffrey Dissmann

References

Genest, C. and A. C. Favre (2007). Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering, 12 (4), 347-368.

See Also

BiCopPar2Tau, BiCopTau2Par, BiCopSelect, CDVineCopSelect

Examples

## Example 1: Gaussian copula with large dependence parameter
par1 = 0.7
fam1 = 1
dat1 = BiCopSim(500,fam1,par1)

# perform the asymptotic independence test
BiCopIndTest(dat1[,1],dat1[,2])


## Example 2: Gaussian copula with small dependence parameter
par2 = 0.01
fam2 = 1
dat2 = BiCopSim(500,fam2,par2)

# perform the asymptotic independence test
BiCopIndTest(dat2[,1],dat2[,2])

Example output

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.

$statistic
[1] 17.07129

$p.value
[1] 0

$statistic
[1] 1.060459

$p.value
[1] 0.288936

CDVine documentation built on May 2, 2019, 9:28 a.m.