Central limit theorem for Wilcoxon rank statistics process

The rank statistics S.N=N.1.Ni=1cNiR.Ni, with RDeltaNi being the rank of XNi+.dNi,i=1,2,.,N and XN1,.,XNN being the random sample from the basic distribution with density function f, are considered as a random process with . in the role of parameter. Under some assumptions on CNi's, dNi's and on the underlying distribution, it is proved that the process {S.N.S0N.ES.N;0...1}, being properly standardized, converges weakly to the Gaussian process with covariances proportional to the product of parameter values. Under additional assumptions, .bN can be written instead of ES.N, where bN=.Ni=1CNidNi.f2(x)dx. As an application, this result yields the asymptotic normality of the standardized form of the length of a confidence interval for regression coefficient based on statistic S.N.