Asymptotic delay times of sequential tests based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e519" altimg="si2.svg"><mml:mi>U</mml:mi></mml:math>-statistics for early and late change points

Sequential change point tests aim at giving an alarm as soon possible after a structural break has occurred while controlling the asymptotic false rate. For such it is of particular importance to understand how quickly detected. In this paper, we derive distribution delay times for sequential procedures based on U-statistics. This includes difference-of-means (DOM) test that been discussed previously but also new robust Wilcoxon test. Based these results can compare detection both instead having rely simulations only. Indeed, procedure smaller heavier tailed distributions which confirmed by simulations. While in previous literature DOM only early points were obtained, well late points. Finally, evaluate approximates actual stopping finite samples via simulation study.