[en] This paper aims to investigate the constraints on dependence measures based on the concept
of concordance when discrete random variables are involved. The main technical argument
consists in a continuous extension of integer-valued random variables by convolution with
unit support kernels
Disciplines :
Mathematics
Author, co-author :
Denuit, Michel
Lambert, Philippe ; Université de Liège - ULiège > Institut des sciences humaines et sociales > Méthodes quantitatives en sciences sociales
Language :
English
Title :
Constraints on concordance measures in bivariate discrete data
Publication date :
2005
Journal title :
Journal of Multivariate Analysis
ISSN :
0047-259X
eISSN :
1095-7243
Publisher :
Academic Press
Volume :
93
Pages :
40-57
Peer reviewed :
Peer Reviewed verified by ORBi
Name of the research project :
IAP research network nr P5/ 24
Funders :
Belgian State (Federal Office for Scientific, Technical and Cultural Affairs)
Agresti A. An Introduction to Categorical Data Analysis 1996 Wiley New York
Goodman L.A. Kruskal W.H. Measures of association for cross classifications J. Amer. Statist. Assoc. 49 1954 732-764
Kendall M.G. The treatment of ties in rank problems Biometrika 33 1945 239-251
A.W. Marshall, Copulas, marginals and joint distributions functions, in: L. Ruschendorf, B. Schweizer, M.D. Taylor (Eds.), Distributions with Fixed Marginals and Related Topics, IMS Lecture Notes, Monograph Series, Vol. 28, Institute of Mathematical Statistics, Hayward, CA, 1996, 213-222.
Nelsen R.B. An Introduction to Copulas 1998 Springer New York
Scarsini M. On measures of concordance Stochastica 8 1984 201-218
Schweizer B. Wolff E.F. On nonparametric measures of dependence for random variables Ann. Statist. 9 1981 879-885
Sklar A. Fonctions de répartitions à n dimensions et leurs marges Publ. Inst. Statist. Univ. Paris 8 1959 229-231
Somers R.H. A new asymmetric measure of association for ordinal variables Amer. Sociol. Rev. 27 1962 799-811
Stevens W.L. Fiducial limits of the parameter of a discontinuous distribution Biometrika 37 1950 117-129
Stuart A. The estimation and comparison of strengths of association in contingency tables Biometrika 40 1953 105-110
Tchen A.H. Inequalities for distributions with given marginals Ann. Probab. 8 1980 814-827
F. Vandenhende, P. Lambert, Modeling repeated ordered categorical data using copulas, Discussion Paper 00-25 Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium, 2000, ftp://www.stat.ucl.ac.be/pub/papers/dp/dp00/dp0025.ps
Vandenhende F. Lambert P. Improved rank-based dependence measures for categorical data Statist. Probab. Lett. 63 2003 157-163
Yanagimoto T. Okamoto M. Partial orderings of permutations and monotonicity of a rank correlation statistic Ann. Inst. Statist. Math. 21 1969 489-506
