The weak convergence of weighted empirical cumulatives based on the ranks of independent, not necessarily identically distributed, observations to a continuous Gaussian process is proved. The results contain a shorter proof of a central limit theorem by Dupac and Hajek (1969) Ann. Math. Statist. Analogous results are proved for signed rank processes.
Hira Lal Koul. Robert G. Staudte Jr.. "Weak Convergence of Weighted Empirical Cumulatives Based on Ranks." Ann. Math. Statist. 43 (3) 832 - 841, June, 1972. https://doi.org/10.1214/aoms/1177692549