Abstract: | Let X1,…, Xn be i.i.d. random variables symmetric about zero. Let Ri(t) be the rank of |Xi − tn−1/2| among |X1 − tn−1/2|,…, |Xn − tn−1/2| and Tn(t) = Σi = 1nφ((n + 1)−1Ri(t))sign(Xi − tn−1/2). We show that there exists a sequence of random variables Vn such that sup0 ≤ t ≤ 1 |Tn(t) − Tn(0) − tVn| → 0 in probability, as n → ∞. Vn is asymptotically normal. |