Second-order linearity of the general signed-rank statistic (Q1095527)

For n independent and identically distributed random variables each drifted by the amount t/\(\sqrt{n}\), let \(T_ n(t)\) denote the usual signed rank statistic. It is shown that uniformly in the closed interval \(t\in [0,1]\), \(T_ n(t)-T_ n(0)-tV_ n\) converges in probability to 0 (as \(n\to \infty)\) where \(V_ n\) has asymptotically a normal distribution. The result is very useful for the study of the asymptotic properties of rank estimators of location and related functionals.