Geodesic
On the connection between cherry-tree copulas and truncated R-vine copulas
Kybernetika, Tome 53 (2017) no. 3, pp. 437-460

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Vine copulas are a flexible way for modeling dependences using only pair-copulas as building blocks. However if the number of variables grows the problem gets fastly intractable. For dealing with this problem Brechmann at al. proposed the truncated R-vine copulas. The truncated R-vine copula has the very useful property that it can be constructed by using only pair-copulas and a lower number of conditional pair-copulas. In our earlier papers we introduced the concept of cherry-tree copulas. In this paper we characterize the relation between cherry-tree copulas and truncated R-vine copulas. It turns out that the concept of cherry-tree copula is more general than the concept of truncated R-vine copula. Although both contain in their expressions conditional independences between the variables, the truncated R-vines constructed in greedy way do not exploit the existing conditional independences in the data. We give a necessary and sufficient condition for a cherry-tree copula to be a truncated R-vine copula. We introduce a new method for truncated R-vine modeling. The new idea is that in the first step we construct the top tree by exploiting conditional independences for finding a good-fitting cherry-tree of order $k$. If this top tree is a tree in an R-vine structure then this will define a truncated R-vine at level $k$ and in the second step we construct a sequence of trees which leads to it. If this top tree is not a tree in an R-vine structure then we can transform it into such a tree at level $k+1$ and then we can again apply the second step. The second step is performed by a backward construction named Backward Algorithm. This way the cherry-tree copulas always can be expressed by pair-copulas and conditional pair-copulas.
DOI : 10.14736/kyb-2017-3-0437
Classification : 60C05, 62H05
Keywords: copula; conditional independences; Regular-vine; truncated vine; cherry-tree copula 
@article{10_14736_kyb_2017_3_0437,
     author = {Kov\'acs, Edith and Sz\'antai, Tam\'as},
     title = {On the connection between cherry-tree copulas and truncated {R-vine} copulas},
     journal = {Kybernetika},
     pages = {437--460},
     publisher = {mathdoc},
     volume = {53},
     number = {3},
     year = {2017},
     doi = {10.14736/kyb-2017-3-0437},
     mrnumber = {3684679},
     zbl = {06819617},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-3-0437/}
}
TY  - JOUR
AU  - Kovács, Edith
AU  - Szántai, Tamás
TI  - On the connection between cherry-tree copulas and truncated R-vine copulas
JO  - Kybernetika
PY  - 2017
SP  - 437
EP  - 460
VL  - 53
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-3-0437/
DO  - 10.14736/kyb-2017-3-0437
LA  - en
ID  - 10_14736_kyb_2017_3_0437
ER  - 
%0 Journal Article
%A Kovács, Edith
%A Szántai, Tamás
%T On the connection between cherry-tree copulas and truncated R-vine copulas
%J Kybernetika
%D 2017
%P 437-460
%V 53
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-3-0437/
%R 10.14736/kyb-2017-3-0437
%G en
%F 10_14736_kyb_2017_3_0437
Kovács, Edith; Szántai, Tamás. On the connection between cherry-tree copulas and truncated R-vine copulas. Kybernetika, Tome 53 (2017) no. 3, pp. 437-460. doi: 10.14736/kyb-2017-3-0437

Cité par Sources :