Functions of Concordance and Dependence with Related Measures

References

• D'all Aglio , G. ( 1972 ). Frechet classes and compatibility of distribution functions . Sympos. Math. 9 : 131 – 150 .
   Google Scholar
• Behboodian , J. , Dolati , A. , Ubeda-Flores , M. ( 2005 ). Measures of association based on average quadrant dependence . J. Probab. Stat. Sci. 3 : 161 – 173 .
   Google Scholar
• Block , H. W. , Fang , Z. ( 1988 ). A multivariate extension of Hoeffding's lemma . Ann. Probab. 16 : 1803 – 1820 .
   Web of Science ®Google Scholar
• Block , H. W. , Savits , T. , Shaked , M. ( 1982 ). Some concepts of negative dependence . Ann. Probab. 10 : 765 – 772 .
   Web of Science ®Google Scholar
• Cambanis , S. , Simons , G. , Stout , W. ( 1976 ). Inequalities for E k (X, Y) when the marginals are fixed . Z. Wahrsch. Verw. Gebiete. 36 : 285 – 294 .
   Web of Science ®Google Scholar
• Cuadras , C. M. ( 2006 ). The importance of being the upper bound in the bivariate family . SORT 31 : 99 – 100 .
   Google Scholar
• Cuadras , C. M. ( 2007 ). On the covariance between functions . J. Multivariate Anal. 81 : 19 – 27 .
   Google Scholar
• Cuadras , C. M. , Dolati , A. ( 2007 ). Correction on “The importance of being the upper bound in the bivariate family” . SORT 31 ( 1 ): 99 – 100 .
   Google Scholar
• Esary , J. D. , Prochan , F. ( 1972 ). Relationships among some concepts of bivariate dependence . Ann. Math. Statist. 43 : 651 – 655 .
   Google Scholar
• Fréchet , M. ( 1935 ). Généralizations du théorème des probabiltés totales . Fund. Math. 25 : 370 – 387 .
   Google Scholar
• Fréchet , M. ( 1951 ). Sur les tableau de corrélation dont les marges sont donneés . Ann. Univ. Lyon Sect. A 9 : 53 – 77 .
   Google Scholar
• Gurrera , M. D. C. ( 2005 ). Construction of bivariate distributions and statistical dependence operations. Ph.D. Dissertation, Department of Statistics, University of Barcelona, Barcelona, Spain .
   Google Scholar
• Hoeffding , W. ( 1940 ). Masstabinvariante korrelationtheorie. Schriften des Matematischen Instituts und des Instituts fur Angewandte Mathematik der Universit t Berlin 5 Heft 3:179–233 .
   Google Scholar
• Hoeffding , W. ( 1941 ). Masstabinvariante korrelationmasse für diskontinuie-liche Vertailungen . Archiv für Matematischen Wirtschaften und Sozialforschung 7 : 49 – 70 .
   Google Scholar
• Hutchinson , T. P. , Lai , C. D. ( 1991 ). Continuous Bivariate Distribution. Emphasizing Applications . Adelaide : Rumsby Scientific Publishing .
   Google Scholar
• Joe , H. ( 1997 ). Multivariate Models and Dependence Concepts . London : Chapman and Hall .
   Google Scholar
• Jogdeo , K. ( 1982 ). Concepts of dependence . In: Kotz , S. , Johnson , N. L. , eds. Encyclopedia of Statistical Sciences . Vol. I . New York : John Wiley & Sons , pp. 324 – 334 .
   Google Scholar
• Kimeldorf , G. , Sampson , A. ( 1978 ). Monotone dependence . Ann. Statist. 6 : 895 – 903 .
   Web of Science ®Google Scholar
• Kimeldorf , G. , Sampson , A. (1987). Positive dependence orderings. Ann. Inst. Statist. Math. 39:113–128.
   Web of Science ®Google Scholar
• Kruskal , W. H. ( 1958 ). Ordinal measures of association . J. Amer. Statist. Assoc. 53 : 814 – 861 .
   Web of Science ®Google Scholar
• Lehmann , E. L. ( 1966 ). Some concepts of dependence . Ann. Math. Statist. 37 : 1137 – 1153 .
   Google Scholar
• Mardia , K. V. , Thompson , J. W. ( 1972 ). A unified treatment of moment-formulae . Sanky: Ind. J. Statis. Ser. A 34 : 121 – 132 .
   Google Scholar
• Nelsen , R. B. ( 2006 ). An Introduction to Copulas. , 2nd ed. New York : Springer Science+ Business Media Inc .
   Google Scholar
• Rényi , A. ( 1959 ). On measures of dependence . Acta. Math. Acad. Sci. Hungar 10 : 441 – 451 .
   Google Scholar
• Scarsini , M. ( 1984 ). On measures of concordance . Stochastica 8 : 201 – 218 .
   Google Scholar
• Schweizer , B. , Wolff , E. F. ( 1981 ). On nonparametric measures of dependence for random variables . Ann. Statist. 9 : 870 – 885 .
   Google Scholar
• Sklar , A. ( 1959 ). Fonctions de répartition à n dimension et leurs marges . Publ. Inst. Statist. Univ. Paris. 8 : 229 – 231 .
   Google Scholar
• Tchen , A. H. ( 1980 ). Inequalities for distributions with given marginals . Ann. Probab. 8 : 814 – 827 .
   Web of Science ®Google Scholar
• Yanagimoto , T. ( 1972 ). Families of positively dependent variables . Ann. Inst. Statist. Math. 24 : 559 – 673 .
   Web of Science ®Google Scholar
• Yanagimoto , T. ( 1990 ). Dependence orderings in statistical models and other notions . In: Block , H. W. , Sampson , A. R. , Savits , T. H. , eds. Topics in Statistical Dependence . Hayward , CA : Institute of Mathematical Statistics .
   Google Scholar
• Yanagimoto , T. , Okamoto , M. ( 1969 ). Partial orderings of permutations and monotonicity of rank correlation statistic . Ann. Inst. Statist. Math. 21 : 489 – 506 .
   Web of Science ®Google Scholar