madogram {ExtremalDep} | R Documentation |
Madogram-based estimation of the Pickands Dependence Function
Description
Computes a non-parametric estimate Pickands dependence function, for multivariate data, based on the madogram estimator.
Usage
madogram(w, data, margin = c("emp","est","exp","frechet","gumbel"))
Arguments
w |
|
data |
|
margin |
string, denoting the type marginal distributions ( |
Details
The estimation procedure is based on the madogram as proposed in Marcon et al. (2017). The madogram is defined by
where and
.
Each row of the design matrix w
is a point in the unit
d
-dimensional simplex.
If is a
d
-dimensional max-stable distributed random vector, with exponent measure function and Pickands dependence function
, then
where
.
From this, it follows that
and
An empirical transformation of the marginals is performed when margin="emp"
.
A max-likelihood fitting of the GEV distributions is implemented when margin="est"
.
Otherwise it refers to marginal parametric GEV theorethical distributions (margin="exp", "frechet", "gumbel"
).
Value
A numeric vector of estimates.
Author(s)
Simone Padoan, simone.padoan@unibocconi.it, https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, borisberanger@gmail.com https://www.borisberanger.com; Giulia Marcon, giuliamarcongm@gmail.com
References
Marcon, G., Padoan, S.A., Naveau, P., Muliere, P. and Segers, J. (2017) Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials. Journal of Statistical Planning and Inference, 183, 1-17.
Naveau, P., Guillou, A., Cooley, D., Diebolt, J. (2009) Modelling pairwise dependence of maxima in space, Biometrika, 96(1), 1-17.
See Also
Examples
x <- simplex(2)
data <- evd::rbvevd(50, dep = 0.4, model = "log", mar1 = c(1,1,1))
Amd <- madogram(x, data, "emp")
Amd.bp <- beed(data, x, 2, "md", "emp", 20, plot=TRUE)
lines(x[,1], Amd, lty = 1, col = 2)