Evaluating copula density --> NaN and inaccuracies

[mcwachter]

Hello,
I got problems evaluating the copula density of vines. To be precise, it occurs that dvinecop returns a NaN. I wrote a small reproducible example:

ncol=30
nrow=10
set.seed(123)
data=matrix(rnorm(nrow*ncol),ncol=ncol)
vine=vinecop(pseudo_obs(data))
res=dvinecop(rep(0,ncol),vine)
print(res)

settingncol=20 or nrow=20 leads to result of 0 and not NaN. So this might be a problem for large p/small n-data. The dataset I am using and where this occured first is also a large p/small n dataset. But the result of exactly 0 is still not satisfactory because it is far away from the correct value 1 (the columns are independent) and it cancels the joint density aswell, since this is the product of copula density and marginal densities.

Many thanks in advance!

[tnagler]

There's are two things at play here. The first is a numerical issue related to the bb7 family, when dependence is strong and the evaluation point near the boundary. That's what caused the NaN and should be fixed here. You can install a package version containing all recent fixes with

devtools::install_github("vinecopulib/rvinecopulib@new-vcl")

The second is a statistical issue not really related to the implementation of our library. If you look at your fitted vine, you will find many non-independence copulas. And if you look at pairwise scatter plots (or correlations) of the data, this shouldn't come at a surprise. With so little data, it's basically impossible to identify the independence copula as the correct model.

The problem is amplified if you have a vine with d > n, where all implemented model selection criteria will provably fail, no matter how large the data set. This issue is discussed in one of my papers and a more suitable criterion is proposed for moderately large d, but it still fails for d > n. So more research is needed...

[tnagler]

New version is on CRAN, I'll close this.

[mcwachter]

Thank you very much.