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Sequential monitoring of high‐dimensional time series

Author

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  • Rostyslav Bodnar
  • Taras Bodnar
  • Wolfgang Schmid

Abstract

In the paper we derive new types of multivariate exponentially weighted moving average (EWMA) control charts which are based on the Euclidean distance and on the distance defined by using the inverse of the diagonal matrix consisting of the variances. The design of the proposed control schemes does not involve the computation of the inverse covariance matrix and, thus, it can be used in the high‐dimensional setting. The distributional properties of the control statistics are obtained and are used in the determination of the new control procedures. Within an extensive simulation study, the new approaches are compared with the multivariate EWMA control charts which are based on the Mahalanobis distance.

Suggested Citation

  • Rostyslav Bodnar & Taras Bodnar & Wolfgang Schmid, 2023. "Sequential monitoring of high‐dimensional time series," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 962-992, September.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:3:p:962-992
    DOI: 10.1111/sjos.12607
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    References listed on IDEAS

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    Cited by:

    1. Yarema Okhrin & Viktoriia Petruk & Wolfgang Schmid, 2025. "Monitoring time dependent image processes for detecting shifts in pixel intensities," Computational Statistics, Springer, vol. 40(9), pages 5225-5256, December.

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