×
Vandenhende, François; Lambert, Philippe

Improved rank-based dependence measures for categorical data. (English) Zbl 1116.62362

Stat. Probab. Lett. 63, No. 2, 157-163 (2003).
Summary: We extend rank-based dependence measures like Spearman’s rho to categorical data so that the same \(\pm 1\) limits are always reached under complete dependence. A goodness-of-fit procedure is derived for dependence models using copulas.

Cited in 6 Documents

MSC:

62H20 Measures of association (correlation, canonical correlation, etc.)
62G10 Nonparametric hypothesis testing

Keywords:

Bivariate ordinal data; Dependence; Copula; Goodness-of-fit test

Software:

bootlib
Cite Review PDF
Full Text: DOI

References:

[1] Agresti, A., Categorical Data Analysis (1990), Wiley Inc: Wiley Inc New York · Zbl 0716.62001
[2] Davison, A. C.; Hinkley, D. V., Bootstrap Methods and Their Application (1997), Cambridge University Press: Cambridge University Press Cambridge, MA · Zbl 0886.62001
[3] Frank, M. J., On the simultaneous associativity of \(F(x,y)\) and \(x+y−F(x,y)\), Aequationes Math., 19, 194-226 (1979) · Zbl 0444.39003
[4] Fréchet, M., Sur les tableaux de corrélation dont les marges sont données, Ann. Univ. Lyon, Sci., 14, 53-77 (1951) · Zbl 0045.22905
[5] Goodman, L. A.; Kruskal, W. H., Measures of association for cross classifications, J. Amer. Statist. Assoc., 49, 732-764 (1954) · Zbl 0056.12801
[6] Schweizer, B.; Wolff, E. F., On nonparametric measures of dependence for random variables, Ann. Statist., 9, 879-885 (1981) · Zbl 0468.62012
[7] Sklar, M., Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris, 8, 229-231 (1959) · Zbl 0100.14202
[8] Tchen, A., Inequalities for distributions with given marginals, Ann. Probab., 8, 814-827 (1980) · Zbl 0459.62010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.