Scalable sum-shrinkage schemes for distributed monitoring large-scale data streams

In this article, we investigate the problem of monitoring independent large-scale data streams where an undesired event may occur at some unknown time and affect only a few unknown data streams. Motivated by parallel and distributed computing, we propose to develop scalable global monitoring schemes by parallel running local detection procedures and by using the sum of the shrinkage transformation of local detection statistics as a global statistic to make a decision. The usefulness of our proposed SUM-Shrinkage approach is illustrated in an example of monitoring large-scale independent normally distributed data streams when the local post-change mean shifts are unknown and can be positive or negative.