Asymptotic normality is established for multivariate linear rank statistics of general type in the non-i.i.d. case covering null hypotheses as well as almost arbitrary alternatives. The functions generating the regression constants and the scores are allowed to have a finite number of discontinuities of the first kind, and to tend to infinity near 0 and 1. The proof is based on properties of empirical df's in the non-i.i.d. case and is patterned on the 1958 Chernoff-Savage method. As special cases e.g. rank statistics used for testing against regression and rank statistics for testing independence are included.
"Asymptotic Normality of Multivariate Linear Rank Statistics in the Non-I.I.D. Case." Ann. Statist. 6 (3) 588 - 602, May, 1978. https://doi.org/10.1214/aos/1176344203