Geodesic
Rates of convergence for a class of rank tests for independence
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 3, Tome 260 (1999), pp. 155-163

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Almost optimal rate of convergence result is obtained for a large class of rank statistics for testing independence including the Gini's and Spearman's rank correlation coefficients as well as the Spearman's footrule. 
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     author = {P. L. Conti and Ya. Yu. Nikitin},
     title = {Rates of convergence for a class of rank tests for independence},
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     volume = {260},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_260_a9/}
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P. L. Conti; Ya. Yu. Nikitin. Rates of convergence for a class of rank tests for independence. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 3, Tome 260 (1999), pp. 155-163. http://geodesic.mathdoc.fr/item/ZNSL_1999_260_a9/