Asymptotic normality of a class of nonlinear rank statistics to test the null hypothesis of total independence of an $m$-variate population is proved. The rank statistics are generated from $2m$-variate square integrable functions such that they are symmetric and nondegenerate. Some results under contiguous alternatives are also given.
"Asymptotic Normality of a Class of Nonlinear Rank Tests for Independence." Ann. Statist. 12 (3) 1124 - 1129, September, 1984. https://doi.org/10.1214/aos/1176346730