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Sufficient reduction in multivariate surveillance

Author

Listed:
  • Frisén, Marianne

    () (Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University)

  • Andersson, Eva

    () (Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University)

  • Schiöler, Linus

    () (Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University)

Abstract

The relation between change points in multivariate surveillance is important but seldom considered. The sufficiency principle is here used to clarify the structure of some problems, to find efficient methods, and to determine appropriate evaluation metrics. We study processes where the changes occur simultaneously or with known time lags. The surveillance of spatial data is one example where known time lags can be of interest. A general version of a theorem for the sufficient reduction of processes that change with known time lags is given. A simulation study illustrates the benefits or the methods based on the sufficient statistics.

Suggested Citation

  • Frisén, Marianne & Andersson, Eva & Schiöler, Linus, 2009. "Sufficient reduction in multivariate surveillance," Research Reports 2009:2, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
  • Handle: RePEc:hhs:gunsru:2009_002
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    File URL: http://hdl.handle.net/2077/20937
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    References listed on IDEAS

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    1. Albert Vexler & Chengqing Wu, 2009. "An Optimal Retrospective Change Point Detection Policy," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 542-558.
    2. S. Knoth, 2002. "Monitoring the mean and the variance of a stationary process," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(1), pages 77-100.
    3. David Bock, 2008. "Aspects on the control of false alarms in statistical surveillance and the impact on the return of financial decision systems," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(2), pages 213-227.
    4. Vasyl Golosnoy, 2007. "Sequential monitoring of minimum variance portfolio," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 91(1), pages 39-55, March.
    5. Bersimis, Sotiris & Psarakis, Stelios & Panaretos, John, 2006. "Multivariate Statistical Process Control Charts: An Overview," MPRA Paper 6399, University Library of Munich, Germany.
    6. Sangyeol Lee & Jeongcheol Ha & Okyoung Na & Seongryong Na, 2003. "The Cusum Test for Parameter Change in Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 781-796.
    7. Frisén, Marianne & Andersson, Eva & Schiöler, Linus, 2007. "Robust outbreak surveillance of epidemics in Sweden," Research Reports 2007:12, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    8. Chu, Chia-Shang James & Stinchcombe, Maxwell & White, Halbert, 1996. "Monitoring Structural Change," Econometrica, Econometric Society, vol. 64(5), pages 1045-1065, September.
    9. Aue, Alexander & Horváth, Lajos, 2004. "Delay time in sequential detection of change," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 221-231, April.
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    More about this item

    Keywords

    change-points; exponential family; MEWMA; monitoring; inference principles;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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