A new approach to the asymptotic normality of simple linear rank statistics for the regression case studied earlier by Hajek (1968) is provided along with the estimation of the remainder term in the approximation to normality.
"Convergence and Remainder Terms in Linear Rank Statistics." Ann. Statist. 5 (4) 671 - 680, July, 1977. https://doi.org/10.1214/aos/1176343891