tic {satdad} | R Documentation |
Tail importance coefficients for Mevlog models.
Description
Computes the tail importance coefficients (tic) on a Mevlog
model which is a multivariate extreme value (symmetric or asymmetric) logistic model, descibed here by its dependence structure.
Usage
tic(ds, ind = 2, n.MC = 1000, sobol = FALSE)
Arguments
ds |
An object of class |
ind |
A character string among "with.singletons" and "all" (without singletons), or an integer in |
n.MC |
Monte Carlo sample size. Default value is 1000. See details in |
sobol |
A boolean. 'FALSE' (the default). If 'TRUE': the index is normalized by the theoretical global variance. |
Details
The tail dependence structure is specified using a ds
object, which corresponds to the stable tail dependence function \ell
.
The process for deducing the stable tail dependence function \ell
from ds
is explained in the Details section of gen.ds
.
The theoretical functional decomposition of the variance of the stdf \ell
consists in writing D(\ell) = \sum_{I \subseteq \{1,...,d\}} D_I(\ell)
where D_I(\ell)
measures the variance of \ell_I(U_I)
the term associated with subset I
in the Hoeffding-Sobol decomposition of \ell
; note that U_I
represents a random vector with independent standard uniform entries.
The theoretical tail importance coefficient (tic) is thus D_I(\ell)
and its sobol version is S_I(\ell)=\dfrac{D_I(\ell)}{D(\ell)}
.
The function tic
uses the Mobius inversion formula, see Formula (8) in Liu and Owen (2006), to derive the tic from the tsic. The latter are the tail superset importance coefficients obtained by the function tsic
.
Value
The function returns a list of two elements:
subsets
A list of subsets from\{1,...,d\}
.When
ind
is given as an integer,subsets
is the list of subsets from\{1,...,d\}
with cardinalityind
.When
ind
is a list, it corresponds tosubsets
.When
ind = "with.singletons"
subsets is the list of all non empty subsets in\{1,...,d\}
.When
ind = "all"
subsets is the list of all subsets in\{1,...,d\}
with cardinality larger or equal to 2.tic
A vector of tail importance coefficients, or their Sobol versions whensobol = "TRUE"
.
Author(s)
Cécile Mercadier (mercadier@math.univ-lyon1.fr
)
References
Liu, R. and Owen, A. B. (2006) Estimating mean dimensionality of analysis of variance decompositions. J. Amer. Statist. Assoc., 101(474):712–721.
Mercadier, C. and Roustant, O. (2019) The tail dependograph. Extremes, 22, 343–372.
See Also
Examples
## Fix a 4-dimensional asymmetric tail dependence structure
ds4 <- gen.ds(d = 4, sub = list(1:2,3:4,1:3))
## Compute all tic values
res4 <- tic(ds4, ind = "with.singletons", sobol = TRUE)
## Check the sum-to-one constraint of tail Sobol indices
sum(res4$tic)