Scalable SUM-Shrinkage Schemes for Distributed Monitoring Large-Scale Data Streams

In this article, motivated by biosurveillance and censoring sensor networks, we investigate the problem of distributed monitoring large-scale data streams where an undesired event may occur at some unknown time and affect only a few unknown data streams. We propose to develop scalable global monitoring schemes by parallel running local detection procedures and by combining these local procedures together to make a global decision based on SUM-shrinkage techniques. Our approach is illustrated in two concrete examples: one is the nonhomogeneous case when the pre-change and post-change local distributions are given, and the other is the homogeneous case of monitoring a large number of independent N(0,1) data streams where the means of some data streams might shift to unknown positive or negative values. Numerical simulation studies demonstrate the usefulness of the proposed schemes.