Geodesic
Multivariate rank correlations: a Gaussian field on a direct product of spheres
Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 2, pp. 236-250

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An asymptotic decision rule of testing for the independence of components of a random vector is suggested. The rule is based on ranking of linear coordinates of observations and on application of Roy's “union-intersection principle”.
Keywords: multivariate sample ranks, Kendall's tau, weak convergence. 
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     author = {V. I. Piterbarg and Yu. N. Tyurin},
     title = {Multivariate rank correlations: a {Gaussian} field on a direct product of spheres},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {236--250},
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     number = {2},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2000_45_2_a1/}
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V. I. Piterbarg; Yu. N. Tyurin. Multivariate rank correlations: a Gaussian field on a direct product of spheres. Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 2, pp. 236-250. http://geodesic.mathdoc.fr/item/TVP_2000_45_2_a1/