Sufficient Reduction in Multivariate Surveillance

Abstract

The relation between change points in multivariate surveillance is important but seldom considered. The sufficiency principle is here used to clarify the structure of some problems, to find efficient methods, and to determine appropriate evaluation metrics. We study processes where the changes occur simultaneously or with known time lags. The surveillance of spatial data is one example where known time lags can be of interest. A general version of a theorem for the sufficient reduction of processes that change with known time lags is given. A simulation study illustrates the benefits or the methods based on the sufficient statistics.

Keywords:

• Change-points
• Exponential family
• Inference principles
• MEWMA
• Monitoring

Mathematics Subject Classification:

• Primary 62B05, 62L10
• Secondary 62C05, 62H99

Acknowledgments

The authors thank Kjell Pettersson for his constructive comments. The work was supported by the Swedish Emergency Management Agency (grant 0314/206).