For testing goodness of fit, we consider a class of U-statistics of overlapping spacings of order two, and investigate their asymptotic properties. The standard U-statistic theory is not directly applicable here as the overlapping spacings form a dependent random sequence. The asymptotic distribution of the statistics under the null hypothesis and under a sequence of local alternatives are derived. In terms of the Pitman ARE, the U-statistic based on Gini's mean square difference of overlapping spacings is found to be the asymptotically locally most powerful. Interestingly, this test has the same efficacy as the Greenwood test based on overlapping spacings.

翻译：为了测试是否合适,我们考虑一组顺序二的重叠间隔的U-统计学,并调查其无症状特性。标准的U-统计学理论在此不直接适用,因为重叠间隔形成一个依附随机序列。根据无效假设和一系列当地替代方法得出了无症状的统计分布。就Pitman ARE而言,基于Gini的重叠间隔平均平方差的U-统计学被认为是局部最强的无症状。有趣的是,这一测试与基于重叠间隔的格林伍德测试同样有效。