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Robust Scan Statistics for Detecting a Local Change in Population Mean for Normal Data

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  • Qianzhu Wu

    (Liberty Mutual Group Inc.)

  • Joseph Glaz

    (University of Connecticut)

Abstract

In this article we investigate the performance of robust scan statistics based on moving medians, as test statistics for detecting a local change in population mean, for one and two dimensional data. When a local change in the population mean has not occurred and outliers are not present in the data, we derive approximations for the tail probabilities of fixed window scan statistics based on moving medians. The performance of the proposed robust scan statistics are evaluated and compared to, via power calculations, the performance of scan statistics based on moving sums, that have been previously investigated in the statistical literature. Numerical results based on a simulation study, for independent and identically distributed (iid) normal observations with known variance, indicate that in presence of outliers the scan statistic based on moving medians outperform the scan statistic based on moving sums, in terms of achieving more accurately the specified probability of type I error. The performance of a multiple window scan statistic based on moving medians for detecting a local change in population mean, for one and two dimensional normal data in presence of outliers, when the size of the window where a change has occurred is unknown has been investigated as well.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:1:d:10.1007_s11009-018-9668-6
    DOI: 10.1007/s11009-018-9668-6
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    References listed on IDEAS

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    1. Xiao Wang & Joseph Glaz, 2014. "Variable Window Scan Statistics for Normal Data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2489-2504, May.
    2. 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.
    3. 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.
    4. G. Haiman & C. Preda, 2006. "Estimation for the Distribution of Two-dimensional Discrete Scan Statistics," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 373-382, 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.
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    Cited by:

    1. 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.

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