We investigate the power of some common change-point tests as a function of the location of the change-point. The test statistics are maxima of weighted U-statistics, with the CUSUM test and the Wilcoxon change-point test as special examples. We study the power under local alternatives, where we vary both the location of the change-point and the magnitude of the change. We quantify in which way weighted versions of the tests are more powerful when the change occurs near the beginning or the end of the time interval, while losing power against changes in the center.

翻译：我们研究了一些常见变点检验的功效作为变点位置的函数。这些检验统计量是加权U统计量的最大值，其中CUSUM检验和Wilcoxon变点检验是特例。我们在局部备择假设下研究功效，其中我们同时改变变点的位置和变化的幅度。我们量化了当变化发生在时间区间起点或终点附近时，检验的加权版本在哪些方面更有效力，而在中心附近的变化中则会损失功效。