Kersting, G. - In: Journal of Multivariate Analysis 21 (1987) 2, pp. 274-295
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) = [Sigma]i = 1n[phi]((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,...</=>