Nonparametric Sequential Monitoring

Abstract The article concerns nonparametric sequential procedures for detection of instabilities in probability distribution in a series of observations. This is a partial survey of procedures based on either ranks, U-statistics, empirical distribution functions, or empirical characteristic functions. Most of the procedures assume that a training (historical) data set is available at the beginning of the monitoring. The main focus is on independent observations but extensions to time series are discussed. In order to derive properties of some procedures either the Anscombe theorem or its generalizations are applied. Most of the presented results can be extended to more general models.

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