Directional dependence of random vectors

In this paper we define and study several properties of the concept of (multivariate) directional dependence and study the new concept in terms of copulas, and provide new measures of multivariate association based on directional dependence. Finally, we show the relationships of directional dependence with other dependence concepts such as association and conditional dependence.

[1]  Moshe Shaked,et al.  A general theory of some positive dependence notions , 1982 .

[2]  Ludger Rüschendorf.  Characterization of dependence concepts in normal distributions , 1981 .

[3]  Mei-Ling Ting,et al.  Some Concepts of Multivariate Dependence. , 1980 .

[4]  Moshe Shaked,et al.  Some Concepts of Negative Dependence , 1982 .

[5]  Manuel Úbeda-Flores,et al.  Multivariate copulas with quadratic sections in one variable , 2008 .

[6]  G. Kimeldorf,et al.  A framework for positive dependence , 1989, Annals of the Institute of Statistical Mathematics.

[7]  H. Bustince,et al.  On the a-migrativity of semicopulas , quasi-copulas , and copulas , 2010 .

[8]  D. Walkup,et al.  Association of Random Variables, with Applications , 1967 .

[9]  Henry W. Block,et al.  Some concepts of mult1variate dependence , 1981 .

[10]  H. Joe.  Multivariate models and dependence concepts , 1998 .

[11]  Piotr Jaworski,et al.  On copulas and their diagonals , 2009, Inf. Sci..

[12]  Michael D. Perlman,et al.  Association of Normal Random Variables and Slepian's Inequality , 1983 .

[13]  R. Nelsen.  An Introduction to Copulas , 1998 .

[14]  Bernard De Baets,et al.  Biconic aggregation functions , 2012, Inf. Sci..

[15]  Moshe Shaked,et al.  Some notions of multivariate positive dependence , 2005 .

[16]  A. Dawid.  Conditional Independence in Statistical Theory , 1979 .

[17]  K. Joag-dev,et al.  Negative Association of Random Variables with Applications , 1983 .

[18]  Y. L. Tong.  The multivariate normal distribution , 1989 .

[19]  Radko Mesiar,et al.  Piecewise linear aggregation functions based on triangulation , 2011, Inf. Sci..

[20]  Malay Ghosh,et al.  Multivariate negative dependence , 1981 .

[21]  E. Lehmann.  Some Concepts of Dependence , 1966 .

[22]  Humberto Bustince,et al.  On the alpha-migrativity of semicopulas, quasi-copulas, and copulas , 2010, Inf. Sci..

[23]  Fabrizio Durante,et al.  On a family of multivariate copulas for aggregation processes , 2007, Inf. Sci..

[24]  M. Sklar.  Fonctions de repartition a n dimensions et leurs marges , 1959 .

[25]  Fabrizio Durante,et al.  New constructions of diagonal patchwork copulas , 2009, Inf. Sci..

[26]  K. Jogdeo.  Characterizations of Independence in Certain Families of Bivariate and Multivariate Distributions , 1968 .

[27]  W. R. Buckland,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1973 .

[28]  Manuel Úbeda-Flores,et al.  Directional dependence in multivariate distributions , 2012 .

[29]  Olga Nánásiová,et al.  Copula and s-map on a quantum logic , 2009, Inf. Sci..