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的变点检验作为变点位置函数的功率。测试统计量是加权U统计量的最大值，其中CUSUM测试和Wilcoxon变点测试是特殊例子。我们研究了局部替代方案下的功率，其中我们改变变点的位置和变化的幅度。我们量化了权重版本的测试方式在变化发生在时间间隔的开头或结尾时更具有优势，但在中心的变化上失去了力量。