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Extensions of some classical methods in change point analysis

Abstract

A common goal in modeling and data mining is to determine, based on sample data, whether or not a change of some sort has occurred in a quantity of interest. The study of statistical problems of this nature is typically referred to as change point analysis. Though change point analysis originated nearly 70 years ago, it is still an active area of research and much effort has been put forth to develop new methodology and discover new applications to address modern statistical questions. In this paper we survey some classical results in change point analysis and recent extensions to time series, multivariate, panel and functional data. We also present real data examples which illustrate the utility of the surveyed results.

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Acknowledgments

We are grateful to Marie Hušková, Stefan Fremdt and the participants of the Time Series Seminar at the University of Utah for pointing out mistakes in the earlier versions of this paper and to Daniela Jarušková and Brad Hatch for some of the data sets.

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Correspondence to Lajos Horváth.

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Research supported by NSF grant DMS 1305858.

This invited paper is discussed in comments available at: doi:10.1007/s11749-014-0367-5, doi:10.1007/s11749-014-0369-3, doi:10.1007/s11749-014-0370-x, doi:10.1007/s11749-014-0371-9, doi:10.1007/s11749-014-0372-8, doi:10.1007/s11749-014-0373-7, doi:10.1007/s11749-014-0376-4, doi:10.1007/s11749-014-0377-3.

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Horváth, L., Rice, G. Extensions of some classical methods in change point analysis. TEST 23, 219–255 (2014). https://doi.org/10.1007/s11749-014-0368-4

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Keywords

  • Change point analysis
  • Sequential monitor
  • Panel data
  • Time series
  • Functional data
  • Linear models

Mathematics Subject Classification

  • Primary 60F017
  • 62M10
  • Secondary 60F05
  • 60F25
  • 62F05
  • 60F12
  • 62G30
  • 62G10
  • 62J05
  • 62L20
  • 62P12
  • 62P20