Directional monitoring and diagnosis for covariance matrices

Abstract

Statistical surveillance for covariance matrices has attracted increasing attention recently. Many approaches have been developed for monitoring general shifts that are arbitrary deviations, as well as sparse shifts occurring in only a few elements. This paper considers directional shifts that occur in only one independent parameter, which is common if the process is relatively stable. A directional covariance matrix control chart is proposed, which fully exploits directional shift information and borrows the strong power of likelihood ratio test. Therefore, this chart provides a powerful tool for monitoring covariance matrices. In addition, the proposed chart does not require specifying the regularisation parameter, and it enjoys a concise quadratic form, thereby easy to implement. Furthermore, this chart naturally leads to a diagnostic prescription for identifying the shifting element in the covariance matrix. Simulation results have demonstrated the efficiency of the suggested control chart and its accompanying diagnostic scheme.

Keywords:

• Direction matrix
• EWMA
• likelihood ratio test
• quadratic form
• statistical process control

Acknowledgments

The authors would like to thank the Editor-in-Chief, the Associate Editor, and two anonymous referees for their many helpful comments that have resulted in significant improvements in this article. Dr. Li's research was supported by the National Key R&D Program of China Grant 2019YFB1704100; the National Natural Science Foundation of China under grant 71772147; the Youth Innovation Team of Shaanxi Universities ‘Big data and Business Intelligent Innovation Team’; and the Fundamental Research Funds for the Central Universities.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Dr. Li's research was supported by the National Key R&D Program of China Grant 2019YFB1704100; the National Natural Science Foundation of China under grant 71772147; the Youth Innovation Team of Shaanxi Universities ‘Big data and Business Intelligent Innovation Team’; and the Fundamental Research Funds for the Central Universities.