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Variable Window Scan Statistics for Normal Data

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  • Xiao Wang
  • Joseph Glaz

Abstract

In this article, approximations and inequalities for the distribution of a two dimensional scan statistic are derived for independently and identically distributed observations from a continuous distribution. The accuracy of these approximations and inequalities is investigated for a normal model. The cases of mean and variance being known and unknown are discussed. Based on approximations for the distributions of one and two dimensional fixed window scan statistics, variable window scan statistics are introduced. We investigate the performance of these variable window scan statistics as test statistics for detection of a local change in the mean of a normal distribution. By utilizing R algorithms for the multivariate normal and t$\mathit {t}$ distributions established by Genz and Bretz (2009), numerical results are presented to evaluate the efficiency of implementing the variable window scan statistics and compare their performance, via power calculations, with fixed window scan statistics. It is evident from the numerical results that if the dimension of the window where a change has occurred is unknown, the variable window scan statistics outperform the fixed window scan statistics.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:10-12:p:2489-2504
    DOI: 10.1080/03610926.2013.782201
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    Citations

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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.
    2. 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.
    3. Jack Noonan & Anatoly Zhigljavsky, 2021. "Approximations for the Boundary Crossing Probabilities of Moving Sums of Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 873-892, September.
    4. 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.
    5. 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.
    6. 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.

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