Rate-Optimal Detection of Very Short Signal Segments
Machine Learning
2014-07-11 v1 Information Theory
math.IT
Statistics Theory
Statistics Theory
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.
Keywords
Cite
@article{arxiv.1407.2812,
title = {Rate-Optimal Detection of Very Short Signal Segments},
author = {T. Tony Cai and Ming Yuan},
journal= {arXiv preprint arXiv:1407.2812},
year = {2014}
}