  The problem of signal detection using sparse, faint information is closely
related to a variety of contemporary statistical problems, including the
control of false-discovery rate, and classification using very high-dimensional
data. Each problem can be solved by conducting a large number of simultaneous
hypothesis tests, the properties of which are readily accessed under the
assumption of independence. In this paper we address the case of dependent
data, in the context of higher criticism methods for signal detection.
Short-range dependence has no first-order impact on performance, but the
situation changes dramatically under strong dependence. There, although higher
criticism can continue to perform well, it can be bettered using methods based
on differences of signal values or on the maximum of the data. The relatively
inferior performance of higher criticism in such cases can be explained in
terms of the fact that, under strong dependence, the higher criticism statistic
behaves as though the data were partitioned into very large blocks, with all
but a single representative of each block being eliminated from the dataset.
