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October 2015 Optimal detection of multi-sample aligned sparse signals
Hock Peng Chan, Guenther Walther
Ann. Statist. 43(5): 1865-1895 (October 2015). DOI: 10.1214/15-AOS1328


We describe, in the detection of multi-sample aligned sparse signals, the critical boundary separating detectable from nondetectable signals, and construct tests that achieve optimal detectability: penalized versions of the Berk–Jones and the higher-criticism test statistics evaluated over pooled scans, and an average likelihood ratio over the critical boundary. We show in our results an inter-play between the scale of the sequence length to signal length ratio, and the sparseness of the signals. In particular the difficulty of the detection problem is not noticeably affected unless this ratio grows exponentially with the number of sequences. We also recover the multiscale and sparse mixture testing problems as illustrative special cases.


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Hock Peng Chan. Guenther Walther. "Optimal detection of multi-sample aligned sparse signals." Ann. Statist. 43 (5) 1865 - 1895, October 2015.


Received: 1 December 2014; Revised: 1 February 2015; Published: October 2015
First available in Project Euclid: 3 August 2015

zbMATH: 1327.62250
MathSciNet: MR3375870
Digital Object Identifier: 10.1214/15-AOS1328

Primary: 62G08 , 62G10

Keywords: Average likelihood ratio , Berk–Jones , higher criticism , Optimal detection , scan statistic , sparse mixture

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 5 • October 2015
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