Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2023, Vol. 40 ›› Issue (1): 41-54.doi: 10.3969/j.issn.1005-3085.2023.01.003

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Statistical Monitoring and Inference of Matrix Time Series Based on 2DPCA

GAO Yuqiao,   XIA Zhiming,   WANG Dan   

  1. School of Mathematics, Northwest University, Xi'an 710127
  • Online:2023-02-15 Published:2023-04-11
  • Contact: Z. Xia. E-mail address: statxzm@nwu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11771353; 12171391).

Abstract:

In the field of multivariate statistical process control, more and more scholars begin to pay attention to the online monitoring of matrix data. Matrix data can usually be reshaped into vector data and then monitored, but the reshape operation destroys the original structure information of matrix data. The 2DPCA method directly extracts the features of the matrix data and can retain the structural features of the matrix. Therefore, it is meaningful to use the 2DPCA method to study the statistically monitoring and inference of the matrix data time series. Based on the 2DPCA method, an orthogonal projection is performed on the matrix data to obtain features, and the monitoring statistics are constructed by using these features. Finally, it is proved that the limit distribution of the monitoring statistics is Chi-square distribution, and the statistical inference is carried out by using this distribution. Simulation experiments show that the method is theoretically correct, and when the sample size is large, the proposed method performs better than similar methods.

Key words: change point, PCA, 2DPCA, matrix normal distribution, Chi-square distribution

CLC Number: