Tests of Multivariate Independence for Ordinal Data

References

• Adler , L. M. ( 1957 ). A modification of Kendall's tau for the case of arbitrary ties in both rankings . J. Amer. Statist. Assoc. 52 : 33 – 35 .
   Web of Science ®Google Scholar
• Agresti , A. ( 2007 ). An Introduction to Categorical Data Analysis. , 2nd ed . Wiley Series in Probability and Statistics . Hoboken , NJ : Wiley-Interscience .
   Google Scholar
• Borkowf , C. B. ( 2002 ). Computing the nonnull asymptotic variance and the asymptotic relative efficiency of Spearman's rank correlation . Computat. Statist. Data Anal. 39 : 271 – 286 .
   Web of Science ®Google Scholar
• Carr , G. J. , Hafner , K. B. , Koch , G. G. ( 1989 ). Analysis of rank measures of association for ordinal data from longitudinal studies . J. Amer. Statist. Assoc. 84 : 797 – 804 .
   Web of Science ®Google Scholar
• Denuit , M. , Lambert , P. ( 2005 ). Constraints on concordance measures in bivariate discrete data . J. Multivariate Anal. 93 : 40 – 57 .
   Web of Science ®Google Scholar
• Essaadouni , O. ( 2007 ). Quelques Généralisation Des Mesures d’association de Kendall et de Spearman Pour Des Données Discrètes Multivariées. Master's thesis, Université du Québec à Trois-Rivières, Québec, Canada .
   Google Scholar
• Genest , C. , Quessy , J.-F. , Rémillard , B. ( 2006 ). Local efficiency of a Cramér–von Mises test of independence . J. Multivariate Anal. 97 : 274 – 294 .
   Google Scholar
• Genest , C. , Quessy , J.-F. , Rémillard , B. ( 2007 ). Asymptotic local efficiency of Cramér–von Mises tests for multivariate independence . Ann. Statist. 35 : 166 – 191 .
   Web of Science ®Google Scholar
• Ghent , A. W. ( 1984 ). Examination of five tau variants suited to ordered contingency tables, from the viewpoint of biological research . American Midland Naturalist 112 : 332 – 368 .
   Google Scholar
• Goodman , A. , Kruskal , W. H. ( 1979 ). Measures of Association for Cross Classifications. Springer Series in Statistics. New York-Berlin : Springer-Verlag .
   Google Scholar
• Hájek , J. , Šidák , Z. ( 1967 ). Theory of Rank Tests. New York : Academic Press .
   Google Scholar
• Hoeffding , W. ( 1948 ). A class of statistics with asymptotically normal distribution . Ann. Mathemat. Statist. 19 : 293 – 325 .
   Google Scholar
• Joe , H. ( 1990 ). Multivariate concordance . J. Multivariate Anal. 35 : 12 – 30 .
   Web of Science ®Google Scholar
• Johnson , N. L. , Kotz , S. , Balakrishnan , N. ( 1997 ). Discrete Multivariate Distributions. New York : John Wiley & Sons .
   Google Scholar
• Karlis , D. ( 2003 ). An EM algorithm for multivariate Poisson distribution and related models . J. Appl. Statist. 30 : 63 – 77 .
   Web of Science ®Google Scholar
• Kendall , M. G. ( 1938 ). A new measure of rank correlation . Biometrika 30 : 8193 .
   Google Scholar
• Lee , A. J. ( 1990 ). U-Statistics. Theory and Practice. Statistics : Textbooks and Monographs, 110 . New York : Marcel Dekker, Inc .
   Google Scholar
• Lehmann , E. L. ( 1966 ). Some concepts of dependence . Ann. Mathemat. Statist. 37 : 1137 – 1153 .
   Google Scholar
• Mesfioui , M. , Tajar , A. ( 2005 ). On the properties of some nonparametric concordance measures in the discrete case . J. Nonparametric Statist. 17 : 541 – 554 .
   Web of Science ®Google Scholar
• Nikitin , Y. Y. , Stepanova , N. A. ( 2000 ). A generalization of Kendall's tau and the asymptotic efficiency of an independence test based on it . J. Mathemat. Sci. 99 : 1154 – 1160 .
   Google Scholar
• Quessy , J.-F. ( 2009 ). Theoretical efficiency comparisons of independence tests based on multivariate versions of Spearman's rho . Metrika . In press .
   Google Scholar
• Ruymgaart , F. H. , van Zuijlen , M. C. A. ( 1978 ). Asymptotic normality of multivariate linear rank statistics in the non-i.i.d. case . Ann. Statist. 6 : 588 – 602 .
   Web of Science ®Google Scholar
• Schmid , F. , Schmidt , R. ( 2007 ). Multivariate extensions of Spearman's rho and related statistics . Statist. Probab. Lett. 77 : 407 – 416 .
   Web of Science ®Google Scholar
• Simon , G. (1977). Multivariate generalization of Kendall's tau with application to data reduction. J. Amer. Statist. Assoc. 72:367–376.
   Google Scholar
• Spearman , C. ( 1904 ). The proof and measurement of association between two things . Amer. J. Psychol. 15 : 88 .
   Google Scholar
• Stepanova , N. A. ( 2003 ). Multivariate rank tests for independence and their asymptotic efficiency . Mathemat. Meth. Statist. 12 : 197 – 217 .
   Google Scholar
• Stuart , A. ( 1953 ). The estimation and comparison of strengths of association in contingency tables . Biometrika 40 : 105 – 110 .
   Web of Science ®Google Scholar