The estimated weighted empirical quantile process is introduced, and under mild regularity conditions is shown to converge weakly in L2(0, 1) to a Gaussian process. This leads to an elementary approach to the derivation of the asymptotic null distribution of Cramér-von Mises type statistics for...

One and two sample rank statistics are shown in general to be more efficient in the Bahadur sense than their sequential rank statistic analogues as defined by Mason (1981, Ann. Statist.9 424-436) and Lombard (1981, South African Statist. J.15 129-152), even though the two families of statistics...

Strong limit theorems are obtained for maximal and minimal multivariate kn-spacings, where {kn}n=1[infinity] is a sequence of positive integers satisfying kn = 0(log n). The shapes, in terms of which these spacings are defined, are allowed to be quite general. They must only satisfy certain...