Minimax Rate Optimal Detection And Identification of Sparse Signal Segments
Tony Cai and Ming Yuan
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Abstract:
Motivated by a range of applications in genomics and engineering, we consider in this paper detection and identification of sparse signal segments in three settings: signals with known shape, arbitrary signals, and smooth signals. Optimal rates of detection are established for the three cases and rate-optimal detectors are constructed. The detectors are easily implementable and are based on scanning with linear and quadratic statistics. Identification of the location of signal segments is also considered. Our analysis reveals both similarities and differences in the strategy and fundamental difficulty of detection and identification among these three settings.
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