Vector correlation based on ranks and a nonparametric test of no association between vectorsFootnote¹

¹Research supported in part by NSERC (Canada), FCAR (Québec) and FRSQ (Québec)

References

• Allaire , J. and Lepage , Y. 1990 . Test de l’absence de liaison entre plusieurs vecteurs aléatoires pour les distributions elliptiques . Statistique et Analyse des Données , 15 ( 3 ) : 21 – 46 .
   Google Scholar
• BMDP Statistical Software, W.J. Dixon . 1981 . Higher transcendental functions , Berkeley : University of California Press . Chief Editor
   Google Scholar
• Cléroux , R. and Ducharme , G.R. 1989 . Vector correlation for elliptical distributions . Comm. in Statist. , A18 ( 4 ) : 1441 – 1454 .
   Google Scholar
• Cléroux , R. , Lazraq , A. and Lepage , Y. 1994 . Indice de redondance basé sur les rangs et inférence non paramétrique . Rev. Statistique Appliquée , LII ( 4 ) : 79 – 98 .
   Google Scholar
• Conover , W.J. and Iman , R.L. 1980 . The rank transformation as a method of discrimination with some examples . Comm. in Statist. , A9 ( 5 ) : 465 – 487 .
   Google Scholar
• Conover , W.J. and Iman , R.L. 1981 . Rank transformation as a bridge between parametric and nonparametric statistics . The American Statistician , 35 : 124 – 133 .
   Web of Science ®Google Scholar
• Coxhead , P. 1974 . Measuring the relationships between two sets of variables . Brit. Jour. Math. Stat. Psycho. , 27 : 205 – 212 .
   Web of Science ®Google Scholar
• Cramer , E.M. 1974 . A generalization of vector correlation and its relation to canonical correlation . Mult. Behav. Res. , 9 : 347 – 352 .
   PubMed Web of Science ®Google Scholar
• Cramer , E.M. and Nicewander , W.A. 1979 . Some symmetric invariant measures of multivariate association . Psychometrika , 44 : 43 – 54 .
   Web of Science ®Google Scholar
• Escoufier , Y. 1973 . Le traitement des variables vectorielles . Biometrics , 29 : 751 – 760 .
   Web of Science ®Google Scholar
• Hoeffding , W. 1948 . A class of statistics with asymptotically normal variables . Ann. Math. Statist. , 19 : 293 – 325 .
   Google Scholar
• Hotelling , H. 1936 . Relations between two sets of variables . Biometrika , 28 : 321 – 377 .
   Web of Science ®Google Scholar
• Imhof , P. 1961 . Computing the distribution of quadratic forms in normal variates . Biometrika , 48 : 419 – 426 .
   Web of Science ®Google Scholar
• Johnson , N.L. and Kotz , S. 1970 . Continuous univariate distributions-2 , Boston : Houghton Mifflin .
   Google Scholar
• Koertz , J. and Abrahamse , A.P.J. 1969 . On the theory and application of the general linear model , Rotterdam : Rotterdam University Press .
   Google Scholar
• Kshirsagar , A.M. 1969 . Correlation between two vector variables . JRSS , B 31 : 477 – 485 .
   Google Scholar
• Puri , M.L. and Sen , P.K. 1971 . Nonparametric methods in multivariate analysis , New York : John Wiley and Sons .
   Google Scholar
• Puri , M.L. , Sen , P.K. and Gokhale , D.V. 1970 . On a class of rank order tests of independence . Sankhya , A : 271 – 298 .
   Google Scholar
• Ramsay , J.O. , ten Berge and Styan , G. 1984 . Matrix correlation . Psychometrika , 49 : 403 – 423 .
   Web of Science ®Google Scholar
• Robert , P. and Escoufier , Y. 1976 . A unifying tool for linear multivariate statistical methods: the RV-coefficient . Appl. Statis. , 25 : 257 – 265 .
   Web of Science ®Google Scholar
• Roseboom , N.W. 1965 . Linear correlation between sets of variables . Psychometrika , 30 : 57 – 71 .
   PubMed Web of Science ®Google Scholar
• Roy , R. and Cléroux , R. 1993 . On vector cross-correlation in time series and application . International Statistical Review , 61 ( no 3 ) : 447 – 464 .
   Web of Science ®Google Scholar
• Shaffer , J.-P. and Gillo , M.W. 1974 . A multivariate extension of the correlation ratio . Educ. Psycho. Meas. , 34 : 521 – 524 .
   Web of Science ®Google Scholar
• Stephens , M. 1979 . Vector correlation . Biometrika , 66 : 41 – 98 .
   Web of Science ®Google Scholar
• Stewart , D. and Love , W. 1968 . A general canonical correlation index . Psycho. Bull. , 70 : 160 – 163 .
   Google Scholar
• Werner , M. , Tolls , M.EM. , Hultin , J.V. and Mellecker , J. 1970 . Sex and Age Dependence of Serum Calcium, Inorganic Phosphorus, Total Protein and Albumin in a Large Ambulatory Population . Fifth International Congress on Automation, Advances in Automated Analysis , 2 : 59 – 65 .
   Google Scholar