  The quickest change detection problem is considered in the context of
monitoring large-scale independent normal distributed data streams with
possible changes in some of the means. It is assumed that for each individual
local data stream, either there are no local changes, or there is a "big" local
change that is larger than a pre-specified lower bound. Two different kinds of
scenarios are studied: one is the sparse post-change case when the unknown
number of affected data streams is much smaller than the total number of data
streams, and the other is when all local data streams are affected
simultaneously although not necessarily identically. We propose a systematic
approach to develop efficient global monitoring schemes for quickest change
detection by combining hard thresholding with linear shrinkage estimators to
estimating all post-change parameters simultaneously. Our theoretical analysis
demonstrates that the shrinkage estimation can balance the tradeoff between the
first-order and second-order terms of the asymptotic expression on the
detection delays, and our numerical simulation studies illustrate the
usefulness of shrinkage estimation and the challenge of Monte Carlo simulation
of the average run length to false alarm in the context of online monitoring
large-scale data streams.
