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Multi-Stage Change Point Detection with Copula Conditional Distribution with PCA and Functional PCA

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  • Jong-Min Kim

    (Division of Science and Mathematics, University of Minnesota-Morris, Morris, MN 56267, USA)

  • Ning Wang

    (Business School, Zhengzhou University, Zhengzhou 450001, China)

  • Yumin Liu

    (Business School, Zhengzhou University, Zhengzhou 450001, China)

Abstract

A global uncertainty environment, such as the COVID-19 pandemic, has affected the manufacturing industry severely in terms of supply and demand balancing. So, it is common that one stage statistical process control (SPC) chart affects the next-stage SPC chart. It is our research objective to consider a conditional case for the multi-stage multivariate change point detection (CPD) model for highly correlated multivariate data via copula conditional distributions with principal component analysis (PCA) and functional PCA (FPCA). First of all, we review the current available multivariate CPD models, which are the energy test-based control chart (ETCC) and the nonparametric multivariate change point model (NPMVCP). We extend the current available CPD models to the conditional multi-stage multivariate CPD model via copula conditional distributions with PCA for linear normal multivariate data and FPCA for nonlinear non-normal multivariate data.

Suggested Citation

  • Jong-Min Kim & Ning Wang & Yumin Liu, 2020. "Multi-Stage Change Point Detection with Copula Conditional Distribution with PCA and Functional PCA," Mathematics, MDPI, vol. 8(10), pages 1-23, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1777-:d:427822
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    References listed on IDEAS

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    1. Liu, Bitao & Müller, Hans-Georg, 2009. "Estimating Derivatives for Samples of Sparsely Observed Functions, With Application to Online Auction Dynamics," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 704-717.
    2. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    3. Brechmann, Eike Christian & Schepsmeier, Ulf, 2013. "Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 52(i03).
    4. Gabor J. Szekely & Maria L. Rizzo, 2005. "Hierarchical Clustering via Joint Between-Within Distances: Extending Ward's Minimum Variance Method," Journal of Classification, Springer;The Classification Society, vol. 22(2), pages 151-183, September.
    5. David S. Matteson & Nicholas A. James, 2014. "A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 334-345, March.
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