期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 60, 期 4, 页码 2217-2232出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2014.2304295
关键词
Hypothesis testing; high-dimensional statistics; sparse mixture; higher criticism; adaptive tests; total variation; Hellinger distance
资金
- 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
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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