| BiCopIndTest {VineCopula} | R Documentation |
Independence Test for Bivariate Copula Data
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 |
Details
The test exploits the asymptotic normality of the test statistic
\texttt{statistic} := T =
\sqrt{\frac{9N(N - 1)}{2(2N + 5)}} \times |\hat{\tau}|,
where N is the number of observations (length of u1) and
\hat{\tau} 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
\texttt{p.value} = 2 \times \left(1 - \Phi\left(T\right)\right),
where \Phi 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
BiCopGofTest(), BiCopPar2Tau(),
BiCopTau2Par(), BiCopSelect(),
RVineCopSelect(), RVineStructureSelect()
Examples
## Example 1: Gaussian copula with large dependence parameter
cop <- BiCop(1, 0.7)
dat <- BiCopSim(500, cop)
# perform the asymptotic independence test
BiCopIndTest(dat[, 1], dat[, 2])
## Example 2: Gaussian copula with small dependence parameter
cop <- BiCop(1, 0.01)
dat <- BiCopSim(500, cop)
# perform the asymptotic independence test
BiCopIndTest(dat[, 1], dat[, 2])