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

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Abstract

In this article we investigate the performance of robust scan statistics based on moving medians, as test statistics for detecting a local change in population mean, for one and two dimensional data. When a local change in the population mean has not occurred and outliers are not present in the data, we derive approximations for the tail probabilities of fixed window scan statistics based on moving medians. The performance of the proposed robust scan statistics are evaluated and compared to, via power calculations, the performance of scan statistics based on moving sums, that have been previously investigated in the statistical literature. Numerical results based on a simulation study, for independent and identically distributed (iid) normal observations with known variance, indicate that in presence of outliers the scan statistic based on moving medians outperform the scan statistic based on moving sums, in terms of achieving more accurately the specified probability of type I error. The performance of a multiple window scan statistic based on moving medians for detecting a local change in population mean, for one and two dimensional normal data in presence of outliers, when the size of the window where a change has occurred is unknown has been investigated as well.

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Acknowledgments

We would like to thank the Associate Editor and the referees for helpful suggestions that improved the presentation of the results in this article.

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Authors and Affiliations

  1. Liberty Mutual Group Inc., Boston, MA, 02116, USA

    Qianzhu Wu

  2. Department of Statistics, University of Connecticut, Storrs, CT, 06269-4120, USA

    Joseph Glaz

Authors
  1. Qianzhu Wu
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  2. Joseph Glaz
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Correspondence to Qianzhu Wu.

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Wu, Q., Glaz, J. Robust Scan Statistics for Detecting a Local Change in Population Mean for Normal Data. Methodol Comput Appl Probab 21, 295–314 (2019). https://doi.org/10.1007/s11009-018-9668-6

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  • DOI: https://doi.org/10.1007/s11009-018-9668-6

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