The sequential change-point detection problem is considered when we are monitoring multiple independent data streams but the post-change distributions involve unknown parameters. One monitoring scheme is the SRRS scheme proposed by Lorden and Pollak (2005) that estimates the post-change parameters by the method of moments (MOM) or maximum likelihood estimators (MLE) of past observations and then uses the Shiryaev-Roberts-type procedure to raise a global alarm. However, it is well-known from the off-line point estimation literature that "shrinkage" often leads to better performances compared to MOM or MLE in the multi-dimensional scenario, see James and Stein (1961), Donoho and Johnstone (1994). Here we propose to adopt two kinds of shrinkage estimators in the SRRS scheme for online monitoring: linear shrinkage for consensus detection and hard thresholding for parallel detection. Our theoretical analysis and numerical simulations demonstrate the usefulness of shrinkage in the sequential or online monitoring setting. Moreover, the SRRS scheme and the shrinkage post-change estimators are also illustrated to be flexible and can be modified to develop a computationally simple scheme when monitoring large-scale data streams.
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