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The aim of online monitoring is to issue an alarm as soon as there issignificant evidence in the collected observations to suggest that theunderlying data generating mechanism has changed. This work is concerned withopen-end, nonparametric procedures that can be interpreted as statisticaltests. The proposed monitoring schemes consist of computing the so-calledretrospective CUSUM statistic (or minor variations thereof) after the arrivalof each new observation. After proposing suitable threshold functions for thechosen detectors, the asymptotic validity of the procedures is investigated inthe special case of monitoring for changes in the mean, both under the nullhypothesis of stationarity and relevant alternatives. To carry out thesequential tests in practice, an approach based on an asymptotic regressionmodel is used to estimate high quantiles of relevant limiting distributions.Monte Carlo experiments demonstrate the good finite-sample behavior of theproposed monitoring schemes and suggest that they are superior to existingcompetitors as long as changes do not occur at the very beginning of themonitoring. Extensions to statistics exhibiting an asymptotic mean-likebehavior are briefly discussed. Finally, the application of the derivedsequential change-point detection tests is succinctly illustrated ontemperature anomaly data.

Open-end nonparametric sequential change-point detection based on the retrospective CUSUM statistic