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Change-point tests based on estimating functions

Wednesday 15th January 2014 - 13:30 to 14:00
INI Seminar Room 1
Many classical change-point tests are based on cumulative sums of estimating functions, where the most prominent example are quasi maximum likelihood scores. Examples include testing for changes in the location model, continuous linear and non-linear autoregressive time series as well as most recently changes in count time series. While classic theory deals with offline procedures where the full data set has been observed before a statistical decision about a change-point is made, the same principles can be used in sequential testing. The latter has gained some increased interest in the last decade, where initial parameter estimation is based on some historic data set with no change-point, before cumulative sum charts are used to monitor newly arriving data. In such a setup, asymptotics are carried out with the size of the historic data set increasing to infinity. In applications such a data set will typically exist as usually at least some data is collected before any reason able statistical inference can be made. In this talk we explain the underlying ideas and extract regularity conditions under which asymptotics both under the null hypothesis as well as alternative can be derived. We will illustrate the usefulness using different examples that have partly already been discussed in the literature.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons