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效力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，以CUSUM检验和Wilcoxon变点检验作为特例。我们研究了局部备择假设下的效力，其中同时改变了变点的位置和变化幅度。我们量化了当变化发生在时间区间起点或终点附近时，加权版本的检验在何种方式下更具效力，同时在对中心区域的变化检验中效力有所损失。