Rate-Optimal Detection of Very Short Signal Segments

T. Tony Cai; Ming Yuan

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arXiv · 1407.2812

Rate-Optimal Detection of Very Short Signal Segments

T. Tony Cai·Ming Yuan

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Abstract

Motivated by a range of applications in engineering and genomics, we consider in this paper detection of very short 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. Our analysis reveals both similarities and differences in the strategy and fundamental difficulty of detection among these three settings.

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BibTeX RIS

T. Tony Cai, Ming Yuan. 2014-07-10. Rate-Optimal Detection of Very Short Signal Segments. https://arxiv.org/abs/1407.2812

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