kdecop() fitCalculates several dependence measures derived from the copula density. All
measures except "blomqvist" are computed by quasi Monte Carlo methods
(see rkdecop().
dep_measures(object, measures = "all", n_qmc = 10^3, seed = 5)
| object | an object of class |
|---|---|
| measures | which measures to compute, see Details. |
| n_qmc | the number of quasi Monte Carlo samples. |
| seed | the seed for quasi Monte Carlo integration. |
A named vector of dependence measures.
The following measures are available:
"kendall"Kendall's \(\tau\), see Nelsen (2007); computed as the sample version of a quasi Monte Carlo sample.
"spearman"Spearman's \(\rho\), see Nelsen (2007); computed as the sample version of a quasi Monte Carlo sample.
"blomqvist"Blomqvist's \(\beta\), see Nelsen (2007); computed as \(4C(0.5, 0.5) - 1\).
"gini"Gini's \(\gamma\), see Nelsen (2007); computed by quasi Monte Carlo integration.
"vd_waerden"van der Waerden's coefficient, see Genest and Verret (2005); computed as the sample version of a quasi Monte Carlo sample.
"minfo"mutual information, see Joe (1989); computed by quasi Monte Carlo integration.
"linfoot"Linfoot's correlation coefficient, see Joe (1989); computed by quasi Monte Carlo integration.
Nelsen, R. (2007). An introduction to copulas. Springer Science & Business Media, 2007.
Genest, C., and Verret, F. (2005). Locally most powerful rank tests of independence for copula models. Journal of Nonparametric Statistics, 17(5)
Joe, H. (1989). Relative Entropy Measures of Multivariate Dependence. Journal of the American Statistical Association, 84(405)
## load data and transform with empirical cdf data(wdbc) udat <- apply(wdbc[, -1], 2, function(x) rank(x) / (length(x) + 1)) ## estimate copula density and calculate dependence measures fit <- kdecop(udat[, 5:6]) dep_measures(fit)#> kendall spearman blomqvist gini vd_waerden minfo linfoot #> 0.4928176 0.6814890 0.4883190 0.5505876 0.6967170 0.3153931 0.6839786