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Sequential change point tests based on U ‐statistics
Author(s) -
Kirch Claudia,
Stoehr Christina
Publication year - 2022
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12558
Subject(s) - cusum , mathematics , change detection , statistical hypothesis testing , statistics , null hypothesis , false alarm , false discovery rate , set (abstract data type) , sequential analysis , limit (mathematics) , point estimation , empirical distribution function , algorithm , computer science , artificial intelligence , gene , programming language , mathematical analysis , biochemistry , chemistry
We propose a general framework of sequential testing procedures based on U ‐statistics which contains as an example a sequential CUSUM test based on differences in mean but also includes a robust sequential Wilcoxon change point procedure. Within this framework, we consider several monitoring schemes that take different observations into account to make a decision at a given time point. Unlike the originally proposed scheme that takes all observations of the monitoring period into account, we also consider a modified moving‐sum‐version as well as a version of a Page‐monitoring scheme. The latter behave almost as good for early changes while being advantageous for later changes. For all proposed procedures we provide the limit distribution under the null hypothesis of no change which yields the threshold to control the global false alarm rate asymptotically. Furthermore, we show that the proposed tests have asymptotic power one. In a simulation study we compare the performance of the sequential procedures via their empirical size, power and detection delay, which is further illustrated by means of a temperature data set.