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Kernel-Based Multivariate Nonparametric CUSUM Multi-Chart for Detection of Abrupt Changes

Author

Listed:
  • Lei Qiao

    (School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China)

  • Bing Wang

    (School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China)

Abstract

In many cases, it is difficult to obtain precise distributional information on multivariate sequences. Therefore, there is a need to propose nonparametric methods for monitoring multivariate sequences. This article discusses the multivariate change detection problem and utilizes the kernel function as the statistic to construct the nonparametric Multivariate Cumulative Sum multi-chart, under the assumption that there is prior information about the abrupt changes. Through theoretical and numerical analysis, we show that the proposed control chart is more effective compared to other existing control charts. The good monitoring effect of this method demonstrates a strong potential for application.

Suggested Citation

  • Lei Qiao & Bing Wang, 2024. "Kernel-Based Multivariate Nonparametric CUSUM Multi-Chart for Detection of Abrupt Changes," Mathematics, MDPI, vol. 12(10), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1473-:d:1391339
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    References listed on IDEAS

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    1. EMROUZNEJAD, Ali & ROSTAMY-MALKHALIFEH, Mohsen & HATAMI-MARBINI, Adel & TAVANA, Madjid, 2012. "General and multiplicative non-parametric corporate performance models with interval ratio data," LIDAM Reprints CORE 2446, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Roozbeh, Mahdi, 2018. "Optimal QR-based estimation in partially linear regression models with correlated errors using GCV criterion," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 45-61.
    3. Zou, Changliang & Qiu, Peihua, 2009. "Multivariate Statistical Process Control Using LASSO," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1586-1596.
    4. Amini, Morteza & Roozbeh, Mahdi, 2015. "Optimal partial ridge estimation in restricted semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 26-40.
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