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Scan Statistics for Detecting a Local Change in Variance for Normal Data with Known Variance

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  • Bo Zhao

    (University of Connecticut)

  • Joseph Glaz

    (University of Connecticut)

Abstract

In this article, several scan statistics are discussed for detecting a local change in variance for one dimensional normal data. When the length of the scanning window is known, a fixed window scan statistic based on moving sum of squares is proposed. Two approximations for the distribution of this scan statistic are investigated. When the length of the scanning window is unknown, a variable window scan statistic based on a generalized likelihood ratio test and a multiple window minimum P-value scan statistic are proposed for detecting the local change in variance. For a moderate or large shift in variance, numerical results indicate that both the variable and multiple window scan statistics perform well. For large data sets, considering the detection power and computing efficiency, the multiple window scan statistic is recommended.

Suggested Citation

  • Bo Zhao & Joseph Glaz, 2016. "Scan Statistics for Detecting a Local Change in Variance for Normal Data with Known Variance," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 563-573, June.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:2:d:10.1007_s11009-015-9465-4
    DOI: 10.1007/s11009-015-9465-4
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    References listed on IDEAS

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    1. D. A. Hsu, 1977. "Tests for Variance Shift at an Unknown Time Point," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(3), pages 279-284, November.
    2. 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.
    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. Loredana Ureche-Rangau & Franck Speeg, 2011. "A simple method for variance shift detection at unknown time points," Economics Bulletin, AccessEcon, vol. 31(3), pages 2204-2218.
    5. Taylor, Jonathan E. & Worsley, Keith J., 2007. "Detecting Sparse Signals in Random Fields, With an Application to Brain Mapping," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 913-928, September.
    6. Andreu Sansó & Vicent Aragó & Josep Lluís Carrion, 2003. "Testing for Changes in the Unconditional Variance of Financial Time Series," DEA Working Papers 5, Universitat de les Illes Balears, Departament d'Economía Aplicada.
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    Cited by:

    1. Jie Chen & Thomas Ferguson & Paul Jorgensen, 2020. "Using Scan Statistics for Cluster Detection: Recognizing Real Bandwagons," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1481-1491, December.

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