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Simultaneous monitoring of process mean vector and covariance matrix via penalized likelihood estimation

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  • Wang, Kaibo
  • Yeh, Arthur B.
  • Li, Bo

Abstract

In recent years, some authors have incorporated the penalized likelihood estimation into designing multivariate control charts under the premise that in practice typically only a small set of variables actually contributes to changes in the process. The advantage of the penalized likelihood estimation is that it produces sparse and more focused estimates of the unknown population parameters which, when used in a control chart, can improve the performance of the resulting control chart. Nevertheless, the existing works focus on monitoring changes occurring only in the mean vector or only in the covariance matrix. Stemming from the ideas of the generalized likelihood ratio test and the multivariate exponentially weighted moving covariance, new control charts are proposed for simultaneously monitoring the mean vector and the covariance matrix of a multivariate normal process. The performance of the proposed charts is assessed by both Monte-Carlo simulations and a real example.

Suggested Citation

  • Wang, Kaibo & Yeh, Arthur B. & Li, Bo, 2014. "Simultaneous monitoring of process mean vector and covariance matrix via penalized likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 206-217.
    • Handle: RePEc:eee:csdana:v:78:y:2014:i:c:p:206-217
    DOI: 10.1016/j.csda.2014.04.017
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    References listed on IDEAS

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    1. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    2. Zhou, Qin & Luo, Yunzhao & Wang, Zhaojun, 2010. "A control chart based on likelihood ratio test for detecting patterned mean and variance shifts," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1634-1645, June.
    3. Maboudou-Tchao, Edgard M. & Agboto, Vincent, 2013. "Monitoring the covariance matrix with fewer observations than variables," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 99-112.
    4. 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.
    5. Jacob Bien & Robert J. Tibshirani, 2011. "Sparse estimation of a covariance matrix," Biometrika, Biometrika Trust, vol. 98(4), pages 807-820.
    6. Bo Li & Kaibo Wang & Arthur Yeh, 2013. "Monitoring the covariance matrix via penalized likelihood estimation," IISE Transactions, Taylor & Francis Journals, vol. 45(2), pages 132-146.
    7. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
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    Cited by:

    1. Manuel Cabral Morais & Wolfgang Schmid & Patrícia Ferreira Ramos & Taras Lazariv & António Pacheco, 2019. "Comparison of joint control schemes for multivariate normal i.i.d. output," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(2), pages 257-287, June.
    2. Nishimura, Kazuya & Matsuura, Shun & Suzuki, Hideo, 2015. "Multivariate EWMA control chart based on a variable selection using AIC for multivariate statistical process monitoring," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 7-13.

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    More about this item

    Keywords

    Likelihood ratio test; L1 penalty function; Penalized likelihood estimation; Phase II monitoring;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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