Minimum Distance Estimators for (Nested) Archimedean Copulas
Compute minimum distance estimators for (nested) Archimedean copulas.
emde(u, cop,
method=c("mde.chisq.CvM", "mde.chisq.KS",
"mde.gamma.CvM", "mde.gamma.KS"),
interval=initOpt(cop@copula@name),
include.K = FALSE, repara = 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 |
|
method |
a
The four methods are described in Hofert et al. (2013); see also the ‘Details’ section. |
interval |
bivariate vector denoting the interval where optimization takes place. The default is computed as described in Hofert et al. (2013). |
include.K |
logical indicating whether the last component, the
(possibly numerically challenging) Kendall distribution function
K, is used ( |
repara |
logical indicating whether the distance function to be optimized is reparametrized (the default); see the code for more details. |
... |
additional arguments passed to |
First, htrafo is applied to map the
n x d-matrix of given realizations to a
n x d-matrix or n x
(d-1)-matrix, depending on whether the last
component is included (include.K=TRUE) or not. Second, using
either the sum of squares of the standard normal quantile function
(method="mde.chisq.CvM" and
method="mde.chisq.KS") or the sum of negative logarithms
(method="mde.gamma.CvM" and method="mde.gamma.KS"), a map to a
chi-square or an Erlang distribution is applied, respectively. Finally, a
Cramér-von Mises (method="mde.chisq.CvM" and
method="mde.gamma.CvM") or Kolmogorov-Smirnov
(method="mde.chisq.KS" and method="mde.gamma.KS") distance is
applied. This is repeated in an optimization until the copula parameter is
found such that this distance is minimized.
Note that the same transformations as described above are applied for goodness-of-fit testing; see the ‘See Also’ section).
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.
Hering, C. and Hofert, M. (2014), Goodness-of-fit tests for Archimedean copulas in high dimensions, Innovations in Quantitative Risk Management.
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)
(meths <- eval(formals(emde)$method)) # "mde.chisq.CvM", ...
fun <- function(meth, u, cop, theta){
run.time <- system.time(val <- emde(u, cop=cop, method=meth)$minimum)
list(value=val, error=val-theta, utime.ms=1000*run.time[[1]])
}
(res <- sapply(meths, fun, u=U, cop=cop, theta=theta))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.