Estimation Procedures for (Nested) Archimedean Copulas
A set of ten different estimators, currently for one-parameter Archimedean copulas, of possibly quite high dimensions.
enacopula(u, cop,
method = c("mle", "smle", "dmle",
"mde.chisq.CvM", "mde.chisq.KS",
"mde.gamma.CvM", "mde.gamma.KS",
"tau.tau.mean", "tau.theta.mean", "beta"),
n.MC = if (method == "smle") 10000 else 0,
interval = initOpt(cop@copula@name),
xargs = list(), ...)u |
n x d-matrix of (pseudo-)observations (each
value in [0,1]) from the copula to be estimated, where n
denotes the sample size and d the dimension. Consider applying the
function |
cop |
|
method |
a
|
n.MC |
only for |
interval |
bivariate vector denoting the interval where
optimization takes place. The default is computed as described in
Hofert et al. (2012). Used for all methods except
|
xargs |
list of additional arguments for the chosen estimation method. |
... |
additional arguments passed to |
enacopula serves as a wrapper for the different
implemented estimators and provides a uniform framework to utilize
them. For more information, see the single estimators as given in the
section ‘See Also’.
Note that Hofert, Mächler, and McNeil (2013) compared these
estimators. Their findings include a rather poor performance and numerically
challenging problems of some of these estimators. In particular, the
estimators obtained by method="mde.gamma.CvM",
method="mde.gamma.KS", method="tau.theta.mean", and
method="beta" should be used with care (or not at all). Overall, MLE
performed best (by far).
the estimated parameter, hat(theta), that is, currently a number as only one-parameter Archimedean copulas are considered.
Hofert, M., Mächler, M., and McNeil, A. J. (2012). Likelihood inference for Archimedean copulas in high dimensions under known margins. Journal of Multivariate Analysis 110, 133–150.
Hofert, M., Mächler, M., and McNeil, A. J. (2013). Archimedean Copulas in High Dimensions: Estimators and Numerical Challenges Motivated by Financial Applications. Journal de la Société Française de Statistique 154(1), 25–63.
emle which returns an object of "mle"
providing useful methods not available for other estimators.
demo(opC-demo) and vignette("GIG", package="copula") for
examples of two-parameter families.
edmle for the diagonal maximum likelihood estimator.
emde for the minimum distance estimators.
etau for the estimators based on Kendall's tau.
ebeta for the estimator based on Blomqvist's beta.
tau <- 0.25
(theta <- copGumbel@iTau(tau)) # 4/3
d <- 12
(cop <- onacopulaL("Gumbel", list(theta,1:d)))
set.seed(1)
n <- 100
U <- rnacopula(n, cop)
meths <- eval(formals(enacopula)$method)
fun <- function(meth, u, cop, theta) {
run.time <- system.time(val <- enacopula(u, cop=cop, method=meth))
list(value=val, error=val-theta, utime.ms=1000*run.time[[1]])
}
t(res <- sapply(meths, fun, u=U, cop=cop, theta=theta))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.