Monitoring procedures for detecting gradual changes (Q6486806)

Considering parametric statistical methods, the underlying model depends on parameters which are (partly) known or must be estimated, e.g., from former data. A standard assumption in these parametric models is that the model parameters are time-invariant. On the other hand, in course of time, changes of the model and its parameters may occur. Hence, the present doctoral thesis deals with the problem of the sequential detection of gradual changes of model parameters. In Chapter 1, general stochastic processes are considered having a linear drift term which shows a possible gradual perturbation at some unknown time point. In Chapter 2, the detection of gradual changes in the location of an unobservable (renewal) process is studied based on observations of the corresponding counting process. The inference is based on the inverse of the counting process, which behaves similarly as the underlying process itself. Following common approaches on detecting gradual changes, in both cases the introduction of detectors and stopping times are studied. Several illustrations and references are given. The present outline of methods for revealing parameter changes in statistical models is suitable for an introduction into this field as well as for further work on this topic.