  The problem of quickest change detection is studied in the context of
detecting an arbitrary unknown mean-shift in multiple independent Gaussian data
streams. The James-Stein estimator is used in constructing detection schemes
that exhibit strong detection performance both asymptotically and
non-asymptotically. First, a James-Stein-based extension of the recently
developed windowed CuSum test is introduced. Our results indicate that the
proposed scheme constitutes a uniform improvement over its typical maximum
likelihood variant. That is, the proposed James-Stein version achieves a
smaller detection delay simultaneously for all possible post-change parameter
values and every false alarm rate constraint, as long as the number of parallel
data streams is greater than three. Additionally, an alternative detection
procedure that utilizes the James-Stein estimator is shown to have asymptotic
detection delay properties that compare favorably to existing tests. The
second-order term of the asymptotic average detection delay is reduced in a
predefined low-dimensional subspace of the parameter space, while second-order
asymptotic minimaxity is preserved. The results are verified in simulations,
where the proposed schemes are shown to achieve smaller detection delays
compared to existing alternatives, especially when the number of data streams
is large.
