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Maximum scan score-type statistics

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  • Glaz, Joseph
  • Zhang, Zhenkui

Abstract

In this article we introduce a maximum scan score-type statistic for testing the null hypothesis that the observations are iid according to a specified distribution, against an alternative that the observations cluster within a window of unknown length. This statistic is a variable window scan statistic, based on a finite number of standardized fixed window scan statistics. Approximations for the significance level of this statistic are derived for 0-1 iid Bernoulli trials and for iid uniform observations on the interval [0,1). The advantage in using a maximum scan score-type statistic, rather than a single fixed window scan statistic, is that it is more effective in detecting window-type clustering of observations.

Suggested Citation

  • Glaz, Joseph & Zhang, Zhenkui, 2006. "Maximum scan score-type statistics," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1316-1322, July.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:13:p:1316-1322
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    References listed on IDEAS

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    1. Chen, Jie & Glaz, Joseph, 2002. "Approximations for a conditional two-dimensional scan statistic," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 287-296, July.
    2. Glaz, Joseph, 1992. "Approximations for tail probabilities and moments of the scan statistic," Computational Statistics & Data Analysis, Elsevier, vol. 14(2), pages 213-227, August.
    3. Vladimir Pozdnyakov & Joseph Glaz & Martin Kulldorff & J. Steele, 2005. "A martingale approach to scan statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 21-37, March.
    4. Joseph Glaz & Zhenkui Zhang, 2004. "Multiple Window Discrete Scan Statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(8), pages 967-980.
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    Cited by:

    1. Marta Benková & Dagmar Bednárová & Gabriela Bogdanovská & Marcela Pavlíčková, 2022. "Redesign of the Statistics Course to Improve Graduates’ Skills," Mathematics, MDPI, vol. 10(15), pages 1-26, July.
    2. Fama, Yuchen & Pozdnyakov, Vladimir, 2011. "A test for self-exciting clustering mechanism," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1541-1546, October.

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