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On the distribution of the T2 statistic, used in statistical process monitoring, for high-dimensional data

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  • Ahmad, M. Rauf
  • Ahmed, S. Ejaz

Abstract

A modification to the asymptotic distribution of the T2-statistic used in multivariate process monitoring is provided when the dimension of the vectors may exceed the sample size. Under certain mild condition, a unified limit distribution is obtained that is applicable for both Phase I and II charts. Further the limit holds for charts based on individual observations as well as subgroup means. The limit is easily applicable and does not need any data preprocessing or dimension reduction. Simulations are used to demonstrate the accuracy of the proposed limit.

Suggested Citation

  • Ahmad, M. Rauf & Ahmed, S. Ejaz, 2021. "On the distribution of the T2 statistic, used in statistical process monitoring, for high-dimensional data," Statistics & Probability Letters, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:stapro:v:168:y:2021:i:c:s0167715220302224
    DOI: 10.1016/j.spl.2020.108919
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    References listed on IDEAS

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    1. 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.
    2. M. Rauf Ahmad, 2017. "Location-invariant Multi-sample U-tests for Covariance Matrices with Large Dimension," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 500-523, June.
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