The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas

被引：54
作者：
Nelsen, RB
Flores, MU
机构：
[1] Lewis & Clark Coll, Dept Math Sci, Portland, OR 97219 USA
[2] Univ Almeria, Dept Estadist & Matemat Aplicada, Almeria 04120, Spain
来源：
COMPTES RENDUS MATHEMATIQUE | 2005年 / 341卷 / 09期
关键词：
D O I：
10.1016/j.crma.2005.09.026
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：583 / 586
页数：4
相关论文
共 6 条
[1]   ON THE CHARACTERIZATION OF A CLASS OF BINARY OPERATIONS ON DISTRIBUTION-FUNCTIONS [J].
ALSINA, C ;
NELSEN, RB ;
SCHWEIZER, B .
STATISTICS & PROBABILITY LETTERS, 1993, 17 (02) :85-89
[2]  
Davey B. A., 2002, INTRO LATTICES ORDER, DOI DOI 10.1017/CBO9780511809088
[3]   A characterization of quasi-copulas [J].
Genest, C ;
Molina, JJQ ;
Lallena, JAR ;
Sempi, C .
JOURNAL OF MULTIVARIATE ANALYSIS, 1999, 69 (02) :193-205
[4]  
Nelsen R. B., 1999, INTRO COPULAS
[5]   Best-possible bounds on sets of bivariate distribution functions [J].
Nelsen, RB ;
Quesada-Molina, JJ ;
Rodríguez-Lallena, JA ;
Ubeda-Flores, M .
JOURNAL OF MULTIVARIATE ANALYSIS, 2004, 90 (02) :348-358
[6]  
Sklar A., 1959, PUBL I STAT U PARIS, V8, P229
1