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Scan Statistics for Normal Data with Outliers

Author

Listed:
  • Qianzhu Wu

    (John Hancock Financial)

  • Joseph Glaz

    (University of Connecticut)

Abstract

In this article we investigate the performance of scan statistics based on moving medians, as test statistics for detecting a local change in population mean, for one and two dimensional normal data, in presence of outliers, when the population variance is unknown. For fixed window scan statistics, both the training sample and parametric bootstrap methods are employed for one and two dimensional normal data, in presence of one or two outliers. Multiple window scan statistics are implemented via the parametric bootstrap method for one and two dimensional normal data, in presence of one or two outliers. Numerical results are presented via simulation to evaluate the power of these scan statistics for detecting the local change in the population mean, for selected parameters of the models characterizing the local change in the population mean and models characterizing the occurrence of one or two outliers in the data. When the window size where the local change of the population mean has occurred is unknown, the multiple window scan statistics, implemented via the bootstrap method, performed quite well.

Suggested Citation

  • Qianzhu Wu & Joseph Glaz, 2021. "Scan Statistics for Normal Data with Outliers," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 429-458, March.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:1:d:10.1007_s11009-020-09837-3
    DOI: 10.1007/s11009-020-09837-3
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    References listed on IDEAS

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    1. Michael V. Boutsikas & Markos V. Koutras, 2000. "Reliability Approximation for Markov Chain Imbeddable Systems," Methodology and Computing in Applied Probability, Springer, vol. 2(4), pages 393-411, December.
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    3. Qianzhu Wu & Joseph Glaz, 2019. "Robust Scan Statistics for Detecting a Local Change in Population Mean for Normal Data," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 295-314, March.
    4. Joseph Glaz & Joseph Naus & Xiao Wang, 2012. "Approximations and Inequalities for Moving Sums," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 597-616, September.
    5. Haiman, George, 1999. "First passage time for some stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 231-248, April.
    6. Sven Fuchs & Christine Ornetsmüller & Reinhold Totschnig, 2012. "Spatial scan statistics in vulnerability assessment: an application to mountain hazards," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 64(3), pages 2129-2151, December.
    7. Wang, Xiao & Zhao, Bo & Glaz, Joseph, 2014. "A multiple window scan statistic for time series models," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 196-203.
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