Dans cette Note, nous montrons que l'ensemble des quasi-copules est un treillis complet, qui est isomorphe au sens de l'ordre à la complétion de Dedekind–MacNeille de l'ensemble des copules. En conséquence, tout ensemble de copules qui possède une propriété statistique particulière est assuré de réaliser les meilleures bornes ponctuelles parmi l'ensemble des quasi-copules.
In this Note we show that the set of quasi-copulas is a complete lattice, which is order-isomorphic to the Dedekind–MacNeille completion of the set of copulas. Consequently, any set of copulas sharing a particular statistical property is guaranteed to have pointwise best-possible bounds within the set of quasi-copulas.
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@article{CRMATH_2005__341_9_583_0, author = {Nelsen, Roger B. and \'Ubeda Flores, Manuel}, title = {The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas}, journal = {Comptes Rendus. Math\'ematique}, pages = {583--586}, publisher = {Elsevier}, volume = {341}, number = {9}, year = {2005}, doi = {10.1016/j.crma.2005.09.026}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.09.026/} }
TY - JOUR AU - Nelsen, Roger B. AU - Úbeda Flores, Manuel TI - The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas JO - Comptes Rendus. Mathématique PY - 2005 SP - 583 EP - 586 VL - 341 IS - 9 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.09.026/ DO - 10.1016/j.crma.2005.09.026 LA - en ID - CRMATH_2005__341_9_583_0 ER -
%0 Journal Article %A Nelsen, Roger B. %A Úbeda Flores, Manuel %T The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas %J Comptes Rendus. Mathématique %D 2005 %P 583-586 %V 341 %N 9 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.09.026/ %R 10.1016/j.crma.2005.09.026 %G en %F CRMATH_2005__341_9_583_0
Nelsen, Roger B.; Úbeda Flores, Manuel. The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas. Comptes Rendus. Mathématique, Tome 341 (2005) no. 9, pp. 583-586. doi : 10.1016/j.crma.2005.09.026. http://archive.numdam.org/articles/10.1016/j.crma.2005.09.026/
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