Model (copula) selection based on k-fold cross-validation
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 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).
xvCopula(copula, x, k = NULL, verbose = interactive(),
ties.method = eval(formals(rank)$ties.method), ...)copula |
object of class |
x |
a data matrix that will be transformed to pseudo-observations. |
k |
the number of data blocks; if |
verbose |
a logical indicating if progress of the cross validation
should be displayed via |
ties.method |
string specifying how ranks should be computed if
there are ties in any of the coordinate samples of |
... |
additional arguments passed to |
A real number equal to the cross-validation criterion multiplied by the sample size.
Note that k-fold cross-validation with k < n
shuffles the lines of x prior to forming the blocks. The
result thus depends on the value of the random seed.
The default estimation method is maximum pseudo-likelihood estimation
but this can be changed if necessary along with all the other
arguments of fitCopula().
Grønneberg, S., and Hjort, N.L. (2014) The copula information criteria. Scandinavian Journal of Statistics 41, 436–459.
## 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)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.