estim.misc {copula} | R Documentation |
Various Estimators for (Nested) Archimedean Copulas, namely,
Method-of-moments-like estimator based on (a multivariate version of) Blomqvist'sbeta.
Maximum likelihood estimator based on the diagonal of a (nested) Archimedean copula.
Method-of-moments-like estimators based on (bivariate) Kendall's tau.
ebeta(u, cop, interval = initOpt(cop@copula@name), ...) edmle(u, cop, interval = initOpt(cop@copula@name), warn=TRUE, ...) etau(u, cop, method = c("tau.mean", "theta.mean"), warn=TRUE, ...)
u |
n x d-matrix of (pseudo-)observations (each value in [0,1]) from the copula, where n denotes the sample size and d the dimension. |
cop |
|
interval |
bivariate vector denoting the interval where optimization takes place. The default is computed as described in Hofert et al. (2013). |
method |
a character string specifying the method (only
for
|
warn |
logical indicating if warnings are printed:
|
... |
additional arguments passed to
|
For ebeta
, the parameter is estimated with a
method-of-moments-like procedure such that the population version of
the multivariate Blomqvist's beta matches its sample version.
Note that the copula diagonal is a distribution function and the
maximum of all components of a random vector following the copula is
distributed according to this distribution function. For
edmle
, the parameter is estimated via maximum-likelihood
estimation based on the diagonal.
For etau
, the method="tau.mean"
means that the average
of sample versions of Kendall's tau are computed first and then the
parameter is determined such that the population version of Kendall's
tau matches this average (if possible); the method="theta.mean"
stands for first computing all pairwise Kendall's tau estimators and
then returning the mean of these estimators.
For more details, see Hofert et al. (2013).
Note that these estimators should be used with care; see the
performance results in Hofert et al. (2013). In particular,
etau
should be used with the (default) method "tau.mean"
since "theta.mean"
is both slower and more prone to errors.
ebeta
the return value of safeUroot
(that is, typically almost the same as the value of
uniroot
) giving the Blomqvist beta estimator.
edmle
list
as returned by
optimize
, including the diagonal maximum likelihood
estimator.
etau
method-of-moments-like estimator based on Kendall's tau for the chosen method.
Marius Hofert
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.
The more sophisticated estimators emle
(Maximum Likelihood) and
emde
(Minimum Distance). enacopula
(wrapper for different estimators).
tau <- 0.25 (theta <- copGumbel@iTau(tau)) # 4/3 d <- 20 (cop <- onacopulaL("Gumbel", list(theta,1:d))) set.seed(1) n <- 200 U <- rnacopula(n, cop) system.time(theta.hat.beta <- ebeta(U, cop=cop)) theta.hat.beta$root system.time(theta.hat.dmle <- edmle(U, cop=cop)) theta.hat.dmle$minimum system.time(theta.hat.etau <- etau(U, cop=cop, method="tau.mean")) theta.hat.etau system.time(theta.hat.etau. <- etau(U, cop=cop, method="theta.mean")) theta.hat.etau.