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

In: Handbook of Scan Statistics

Author

Listed:
  • Jie Chen

    (University of Massachusetts, The Statistical Computing Center)

  • Joseph Glaz

    (University of Connecticut, Department of Statistics)

Abstract

In this article, we review the approximations and inequalities that have been derived in the scientific literature for fixed-, multiple-, and variable-window-length scan statistics, for detecting a local change in the population mean, for one-dimensional normal data. We assume that the variance of the underlying distribution is known and remains unchanged. Monitoring processes based on a fixed-window scan statistic via fixed and sequential sampling schemes are discussed as well. In the context of sequential sampling schemes for the monitoring process, we discuss a repeated significance test and evaluate its properties. The implementation of two multiple-window-length scan statistics are based on the minimum p-value statistic and the generalized likelihood ratio test statistic, respectively. The implementation of the variable-window scan statistic is based on the generalized likelihood ratio test statistic. Simulation algorithms and numerical results are presented to evaluate the performance of the multiple and variable-window-type scan statistics and compare them with fixed-window scan statistics.

Suggested Citation

  • Jie Chen & Joseph Glaz, 2024. "Scan Statistics for Detecting a Local Change in Mean for Normal Data," Springer Books, in: Joseph Glaz & Markos V. Koutras (ed.), Handbook of Scan Statistics, chapter 22, pages 425-450, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-8033-4_21
    DOI: 10.1007/978-1-4614-8033-4_21
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