Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 60, Issue 4, Pages 2217-2232Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2014.2304295
Keywords
Hypothesis testing; high-dimensional statistics; sparse mixture; higher criticism; adaptive tests; total variation; Hellinger distance
Funding
- NSF FRG [DMS-0854973]
- NSF [DMS-1208982]
- NIH [R01 CA127334]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1208982] Funding Source: National Science Foundation
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Detection of sparse signals arises in a wide range of modern scientific studies. The focus so far has been mainly on Gaussian mixture models. In this paper, we consider the detection problem under a general sparse mixture model and obtain explicit expressions for the detection boundary under mild regularity conditions. In addition, for Gaussian null hypothesis, we establish the adaptive optimality of the higher criticism procedure for all sparse mixtures satisfying the same conditions. In particular, the general results obtained in this paper recover and extend in a unified manner the previously known results on sparse detection far beyond the conventional Gaussian model and other exponential families.
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