Spatio-temporal process monitoring using exponentially weighted spatial LASSO

Abstract

Spatio-temporal process monitoring (STPM) has received a considerable attention recently due to its broad applications in environment monitoring, disease surveillance, streaming image processing, and more. Because spatio-temporal data often have complicated structure, including latent spatio-temporal data correlation, complex spatio-temporal mean structure, and nonparametric data distribution, STPM is a challenging research problem. In practice, if a spatio-temporal process has a distributional shift (e.g., mean shift) started at a specific time point, then the spatial locations with the shift are usually clustered in small regions. This kind of spatial feature of the shift has not been considered in the existing STPM literature yet. In this paper, we develop a new STPM method that takes into account the spatial feature of the shift in its construction. The new method combines the ideas of exponentially weighted moving average in the temporal domain for online process monitoring and spatial LASSO in the spatial domain for accommodating the spatial feature of a future shift. It can also accommodate the complicated spatio-temporal data structure well. Both simulation studies and a real-data application show that it can provide a reliable and effective tool for different STPM applications.

Keywords:

• Data correlation
• exponentially weighted moving average
• nonparametric regression
• spatial LASSO
• spatio-temporal data
• variable selection

Acknowledgments

The authors thank the editor, the associate editor, and two referees for many insightful comments and suggestions, which improved the quality of the paper greatly. This research was supported in part by the NSF grant DMS-1914639.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by a grant from the National Science Foundation under grant number DMS-1914639.

Notes on contributors

Peihua Qiu

Peihua Qiu received his Ph.D. in statistics from the Department of Statistics at the University of Wisconsin at Madison in 1996. He worked as a senior research consulting statistician of the Biostatistics Center at the Ohio State University during 1996–1998. He then worked as an assistant professor (1998–2002), associate professor (2002–2007), and full professor (2007–2013) of the School of Statistics at the University of Minnesota. He is an elected fellow of the American Society for Quality, an elected fellow of the American Statistical Association, an elected fellow of the Institute of Mathematical Statistics, an elected member of the International Statistical Institute, and a lifetime member of the International Chinese Statistical Association. He served as an associate editor for Journal of the American Statistical Association, Biometrics, Technometrics, Surgery, and Statistical Papers, and guest co-editor for Multimedia Tools and Applications, and Quality and Reliability Engineering International. He was the editor-elect (2013) and editor (2014–2016) of Technometrics. He is currently an associate editor of Quality Engineering, and the Dean’s Professor and Founding Chair of the Department of Biostatistics at the University of Florida.

Peihua Qiu has made substantial contributions in the areas of jump regression analysis, image processing, statistical process control, survival analysis, disease screening, and disease surveillance. So far, he has published over 150 research papers in referred journals, many of which appeared in top journals, including Technometrics, Journal of the American Statistical Association, Annals of Statistics, Annals of Applied Statistics, Journal of the Royal Statistical Society (Series B), Biometrika, Biometrics, IEEE Transactions on Pattern Analysis and Machine Intelligence, Journal of Quality Technology, and IISE Transactions. His research monograph titled Image Processing and Jump Regression Analysis (2005, Wiley) won the inaugural Ziegel prize in 2007 for its contribution in bridging the gap between jump regression analysis in statistics and image processing in computer science. His second book titled Introduction to Statistical Process Control was published in 2014 by Chapman & Hall/CRC.

Kai Yang

Kai Yang received his Ph.D. in biostatistics from the Department of Biostatistics at the University of Florida in 2021. His thesis research was mainly on spatio-temporal data modeling and monitoring under the supervision of Professor Peihua Qiu. He is currently a tenure-track assistant professor of the Division of Biostatistics at the Medical College of Wisconsin at Milwaukee. His major research interests are in statistical process control, spatio-temporal data modeling and monitoring, and statistical applications. He has published about a dozen papers in these areas.