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Denuit, Michel; Lambert, Philippe

Constraints on concordance measures in bivariate discrete data. (English) Zbl 1095.62065

J. Multivariate Anal. 93, No. 1, 40-57 (2005).
Summary: 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.

Cited in 2 Reviews
Cited in 58 Documents

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H20 Measures of association (correlation, canonical correlation, etc.)

Keywords:

Dependence; Concordance; Copula; Bivariate discrete; Kendall’s tau
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\textit{M. Denuit} and \textit{P. Lambert}, J. Multivariate Anal. 93, No. 1, 40--57 (2005; Zbl 1095.62065)
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References:

[1] Agresti, A., An Introduction to Categorical Data Analysis (1996), Wiley: Wiley New York · Zbl 0868.62008
[2] Goodman, L. A.; Kruskal, W. H., Measures of association for cross classifications, J. Amer. Statist. Assoc, 49, 732-764 (1954) · Zbl 0056.12801
[3] Kendall, M. G., The treatment of ties in rank problems, Biometrika, 33, 239-251 (1945) · Zbl 0063.03216
[5] Nelsen, R. B., An Introduction to Copulas (1998), Springer: Springer New York
[6] Scarsini, M., On measures of concordance, Stochastica, 8, 201-218 (1984) · Zbl 0582.62047
[7] Schweizer, B.; Wolff, E. F., On nonparametric measures of dependence for random variables, Ann. Statist, 9, 879-885 (1981) · Zbl 0468.62012
[8] Sklar, A., Fonctions de répartitions à \(n\) dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris, 8, 229-231 (1959)
[9] Somers, R. H., A new asymmetric measure of association for ordinal variables, Amer. Sociol. Rev, 27, 799-811 (1962)
[10] Stevens, W. L., Fiducial limits of the parameter of a discontinuous distribution, Biometrika, 37, 117-129 (1950) · Zbl 0037.36701
[11] Stuart, A., The estimation and comparison of strengths of association in contingency tables, Biometrika, 40, 105-110 (1953) · Zbl 0050.36405
[12] Tchen, A. H., Inequalities for distributions with given marginals, Ann. Probab, 8, 814-827 (1980) · Zbl 0459.62010
[14] Vandenhende, F.; Lambert, P., Improved rank-based dependence measures for categorical data, Statist. Probab. Lett, 63, 157-163 (2003) · Zbl 1116.62362
[15] Yanagimoto, T.; Okamoto, M., Partial orderings of permutations and monotonicity of a rank correlation statistic, Ann. Inst. Statist. Math, 21, 489-506 (1969) · Zbl 0208.44704
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