copula (version 1.1-7)

xvCopula: Model (copula) selection based on k-fold cross-validation

Description

Computes the leave-one-out cross-validation criterion (or a k-fold version of it) for the hypothesized parametric copula family using, by default, maximum pseudo-likelihood estimation.

The leave-one-out criterion is a crossvalidated log likelihood. It is denoted by \(\widehat{xv}_n\) in Grønneberg and Hjort (2014) and defined in equation (42) therein. When computed for several parametric copula families, it is thus meaningful to select the family maximizing the criterion.

For \(k < n\), \(n\) the sample size, the k-fold version is an approximation of the leave-one-out criterion that uses \(k\) randomly chosen (almost) equally sized data blocks instead of \(n\). When \(n\) is large, \(k\)-fold cross-validation is considerably faster (if \(k\) is “small” compared to \(n\)).

Usage

xvCopula(copula, x, k = NULL, verbose = interactive(),
         ties.method = eval(formals(rank)$ties.method), ...)

Value

A real number equal to the cross-validation criterion multiplied by the sample size.

References

Grønneberg, S., and Hjort, N.L. (2014) The copula information criteria. Scandinavian Journal of Statistics 41, 436--459.

See Also

fitCopula() for the underlying estimation procedure and gofCopula() for goodness-of-fit tests.

Examples

set.seed(47)
## A two-dimensional data example ----------------------------------
x <- rCopula(200, claytonCopula(3))


## Model (copula) selection -- takes time: each fits 200 copulas to 199 obs.
xvCopula(gumbelCopula(), x)
xvCopula(frankCopula(), x)
xvCopula(joeCopula(), x)
xvCopula(claytonCopula(), x)
xvCopula(normalCopula(), x)
xvCopula(tCopula(), x)
xvCopula(plackettCopula(), x)


## The same with 5-fold cross-validation [to save time ...]
set.seed(1) # k-fold is random (for k < n) !
xvCopula(gumbelCopula(),  x, k=5)
xvCopula(frankCopula(),   x, k=5)
xvCopula(joeCopula(),     x, k=5)
xvCopula(claytonCopula(), x, k=5)
xvCopula(normalCopula(),  x, k=5)
xvCopula(tCopula(),       x, k=5)
xvCopula(plackettCopula(),x, k=5)