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

Qianzhu Wu () and Joseph Glaz ()
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Qianzhu Wu: Liberty Mutual Group Inc.
Joseph Glaz: University of Connecticut

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 1, 295-314

Abstract: 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.

Keywords: Minimum p-value statistic; Moving mean; Moving median; Multiple window scan statistic; Robust scan statistic; 60G35; 62E17; 62F03; 62F35 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-018-9668-6

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