Statistics sequential testing Offline#

In this setup an additional focus lies in the quick detection of changes after they have occurred. On the other hand, data is collected more and more automatically with data arriving one by one, which requires a different statistical methodology designed to sequentially (online) make a decision after each new observation whether a break is likely to have occurred.

Statistics sequential testing Offline#

So-called a posteriori or offline procedures deal with the testing and segmentation of completely observed data, see for example, Aue and Horváth ( 2013) and Horváth and Rice ( 2014) for two recent survey articles mainly concerned with a posteriori testing or Fryzlewicz ( 2014), Killick et al. ( 2012), Rigaill ( 2015) and Frick et al. ( 2014) to name but a few articles dealing with data segmentation.

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.Ĭhange point and data segmentation procedures have a long tradition in statistics. Furthermore, we show that the proposed tests have asymptotic power one. 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. The latter behave almost as good for early changes while being advantageous for later changes. 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. Within this framework, we consider several monitoring schemes that take different observations into account to make a decision at a given time point. 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.