The class of multivariate Archimedean copulas is defined by using a real-valued function called the generator of the copula. This generator satisfies some properties, including -monotonicity. We propose here a new basic transformation of this generator, preserving these properties, thus ensuring the validity of the transformed generator and inducing a proper valid copula. This transformation acts only on a specific portion of the generator, it allows both the non-reduction of the likelihood on a given dataset, and the choice of the upper tail dependence coefficient of the transformed copula. Numerical illustrations show the utility of this construction, which can improve the fit of a given copula both on its central part and its tail.
Accepté le :
DOI : 10.1051/ps/2017003
Mots clés : Archimedean copulas, transformations, distortions, tail dependence coefficients, likelihood
@article{PS_2017__21__183_0,
author = {Di Bernardino, Elena and Rulli\`ere, Didier},
title = {A note on upper-patched generators for {Archimedean} copulas},
journal = {ESAIM: Probability and Statistics},
pages = {183--200},
publisher = {EDP-Sciences},
volume = {21},
year = {2017},
doi = {10.1051/ps/2017003},
mrnumber = {3716126},
zbl = {1395.62134},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2017003/}
}
TY - JOUR AU - Di Bernardino, Elena AU - Rullière, Didier TI - A note on upper-patched generators for Archimedean copulas JO - ESAIM: Probability and Statistics PY - 2017 SP - 183 EP - 200 VL - 21 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2017003/ DO - 10.1051/ps/2017003 LA - en ID - PS_2017__21__183_0 ER -
%0 Journal Article %A Di Bernardino, Elena %A Rullière, Didier %T A note on upper-patched generators for Archimedean copulas %J ESAIM: Probability and Statistics %D 2017 %P 183-200 %V 21 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2017003/ %R 10.1051/ps/2017003 %G en %F PS_2017__21__183_0
Di Bernardino, Elena; Rullière, Didier. A note on upper-patched generators for Archimedean copulas. ESAIM: Probability and Statistics, Tome 21 (2017), pp. 183-200. doi : 10.1051/ps/2017003. http://www.numdam.org/articles/10.1051/ps/2017003/
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