On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators
We study the impact of certain transformations within the class of Archimedean copulas. We give some admissibility conditions for these transformations, and define some equivalence classes for both transformations and generators of Archimedean copulas. We extend the r-fold composition of the diagona...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2013-01-01
|
| Series: | Dependence Modeling |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/demo-2013-0001 |
| id |
doaj-5b40b9a3e1904dca85d3c32f96e5d984 |
|---|---|
| record_format |
Article |
| spelling |
doaj-5b40b9a3e1904dca85d3c32f96e5d9842021-10-02T19:15:29ZengDe GruyterDependence Modeling2300-22982013-01-011201313610.2478/demo-2013-0001demo-2013-0001On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generatorsDi Bernardino Elena0Rullière Didier1Conservatoire National des Arts et Métiers, Département IMATH, EA4629, 292 rue Saint Martin, 75011, Paris, FranceUniversité de Lyon, Université Lyon 1, ISFA, Laboratoire SAF, EA2429, 50 avenue Tony Garnier, 69366Lyon, FranceWe study the impact of certain transformations within the class of Archimedean copulas. We give some admissibility conditions for these transformations, and define some equivalence classes for both transformations and generators of Archimedean copulas. We extend the r-fold composition of the diagonal section of a copula, from r ∈ N to r ∈ R. This extension, coupled with results on equivalence classes, gives us new expressions of transformations and generators. Estimators deriving directly from these expressions are proposed and their convergence is investigated. We provide confidence bands for the estimated generators. Numerical illustrations show the empirical performance of these estimators.https://doi.org/10.2478/demo-2013-0001transformations of archimedean copulas self-nested diagonalnon-parametric estimation tail dependence62h1262e1762g0562g20 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Di Bernardino Elena Rullière Didier |
| spellingShingle |
Di Bernardino Elena Rullière Didier On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators Dependence Modeling transformations of archimedean copulas self-nested diagonal non-parametric estimation tail dependence 62h12 62e17 62g05 62g20 |
| author_facet |
Di Bernardino Elena Rullière Didier |
| author_sort |
Di Bernardino Elena |
| title |
On certain transformations of Archimedean copulas:
Application to the non-parametric estimation of their
generators |
| title_short |
On certain transformations of Archimedean copulas:
Application to the non-parametric estimation of their
generators |
| title_full |
On certain transformations of Archimedean copulas:
Application to the non-parametric estimation of their
generators |
| title_fullStr |
On certain transformations of Archimedean copulas:
Application to the non-parametric estimation of their
generators |
| title_full_unstemmed |
On certain transformations of Archimedean copulas:
Application to the non-parametric estimation of their
generators |
| title_sort |
on certain transformations of archimedean copulas:
application to the non-parametric estimation of their
generators |
| publisher |
De Gruyter |
| series |
Dependence Modeling |
| issn |
2300-2298 |
| publishDate |
2013-01-01 |
| description |
We study the impact of certain transformations within the
class of Archimedean copulas. We give some admissibility
conditions for these transformations, and define some equivalence
classes for both transformations and generators of
Archimedean copulas. We extend the r-fold composition of
the diagonal section of a copula, from r ∈ N to r ∈ R. This extension,
coupled with results on equivalence classes, gives us
new expressions of transformations and generators. Estimators
deriving directly from these expressions are proposed
and their convergence is investigated. We provide confidence
bands for the estimated generators. Numerical illustrations
show the empirical performance of these estimators. |
| topic |
transformations of archimedean copulas self-nested diagonal non-parametric estimation tail dependence 62h12 62e17 62g05 62g20 |
| url |
https://doi.org/10.2478/demo-2013-0001 |
| work_keys_str_mv |
AT dibernardinoelena oncertaintransformationsofarchimedeancopulasapplicationtothenonparametricestimationoftheirgenerators AT rullieredidier oncertaintransformationsofarchimedeancopulasapplicationtothenonparametricestimationoftheirgenerators |
| _version_ |
1716847584355549184 |