copula (version 0.999-15)

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, denoted $xv^n$, defined in equation (42) of Grønneberg and Hjort (2014).

For $k < n$, $n$ the sample size, the k-fold version uses $k$ randomly chosen (almost) equally sized data blocks instead of $n$. When $n$ is large, $k$-fold is considerably faster (if $k$ is “small” compared to $n$).

Usage

xvCopula(copula, x, k = NULL, verbose = interactive(), ...)

Arguments

copula

object of class "copula" representing the hypothesized copula family.

x

a data matrix that will be transformed to pseudo-observations.

k

the number of data blocks; if k = NULL, nrow(x) blocks are considered (which corresponds to leave-one-out cross-validation).

verbose

a logical indicating if progress of the cross validation should be displayed via txtProgressBar.

...

additional arguments passed to fitCopula().

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

## 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 10-fold cross-validation
set.seed(1) # k-fold is random (for k < n) !
xvCopula(gumbelCopula(),  x, k=10)
xvCopula(frankCopula(),   x, k=10)
xvCopula(joeCopula(),     x, k=10)
xvCopula(claytonCopula(), x, k=10)
xvCopula(normalCopula(),  x, k=10)
xvCopula(tCopula(),       x, k=10)
xvCopula(plackettCopula(),x, k=10)