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Scan statistics for detecting a local change in variance for normal data with unknown population variance

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  • Zhao, Bo
  • Glaz, Joseph

Abstract

In this article we investigate the performance of fixed, multiple and variable window scan statistics in detecting a local change in variance for a sequence of normal observations, when the population variance of the underlying normal distribution is unknown. For fixed window scan statistics, we study: the training sample approach, the conditioning on sufficient statistic approach and the parametric bootstrap testing approach. It is evident from the numerical results that the scan statistic constructed via the conditioning approach outperforms the other two fixed window scan statistics investigated in this article. Based on power calculation presented in this article, one can conclude that when the size of the window where a local change of variance has occurred is unknown, multiple and variable window scan statistics outperform fixed window scan statistics. The multiple and variable window scan statistics perform equally well. When the sequence of observations is large, the implementation of the multiple window scan statistic is computationally more practical.

Suggested Citation

  • Zhao, Bo & Glaz, Joseph, 2016. "Scan statistics for detecting a local change in variance for normal data with unknown population variance," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 137-145.
    • Handle: RePEc:eee:stapro:v:110:y:2016:i:c:p:137-145
    DOI: 10.1016/j.spl.2015.12.020
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    1. G. Haiman & C. Preda, 2002. "A New Method for Estimating the Distribution of Scan Statistics for a Two-Dimensional Poisson Process," Methodology and Computing in Applied Probability, Springer, vol. 4(4), pages 393-407, December.
    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. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    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. 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.
    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.
    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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    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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