Abstract
We present an efficient score statistic, called the statistic, to detect the emergence of a spatially and temporally correlated signal from either fixed-sample or sequential data. The signal may cause a mean shift and/or a change in the covariance structure. The score statistic can capture both the spatial and temporal structures of the change and hence is particularly powerful in detecting weak signals. The score statistic is computationally efficient and statistically powerful. Our main theoretical contribution is accurate analytical approximations to the false alarm rate of the detection procedures, which can be used to calibrate the threshold analytically. Numerical experiments on simulated and real data, as well as a case study of water quality monitoring using sensor networks, demonstrate the good performance of our procedure.
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