Abstract
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.
Original language | English (US) |
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Article number | 6730948 |
Pages (from-to) | 2217-2232 |
Number of pages | 16 |
Journal | IEEE Transactions on Information Theory |
Volume | 60 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2014 |
Externally published | Yes |
Keywords
- Hellinger distance
- Hypothesis testing
- adaptive tests
- high-dimensional statistics
- higher criticism
- sparse mixture
- total variation
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences