Optimal detection of sparse mixtures against a given null distribution

Tony T. Cai, Yihong Wu

Research output: Contribution to journalArticle

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 languageEnglish (US)
Article number6730948
Pages (from-to)2217-2232
Number of pages16
JournalIEEE Transactions on Information Theory
Volume60
Issue number4
DOIs
StatePublished - Apr 2014

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

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