Strong large deviations for Rao test score and GLRT in exponential families

Pierre Moulin, Patrick R. Johnstone

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Exact asymptotics are derived for composite hypothesis testing between two product probability measures Pn vs Qn, subject to a type-I error-probability constraint ϵ. Here P is known but Q is an unknown element of a given d-dimensional regular exponential family. We study the Rao score test, which is a quadratic approximation to the GLRT. The type-II error probability is shown to vanish as equation where D and V are respectively the Kullback-Leibler divergence and the variance of information divergence between P and Q; τ(ϵ; d) is the 1 - ϵ quantile for the χd2 distribution; and the constants βd > 0 and γd are explicitly identified. The asymptotic regret relative to the Neyman-Pearson test (which knows Q) is reflected in the coefficient τ(ϵ; d), as is the cost of dimensionality. Looser asymptotics (with O(1) in place of ϵd) are obtained for the GLRT.

Original languageEnglish (US)
Title of host publicationProceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages779-783
Number of pages5
ISBN (Electronic)9781467377041
DOIs
StatePublished - Sep 28 2015
EventIEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, Hong Kong
Duration: Jun 14 2015Jun 19 2015

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2015-June
ISSN (Print)2157-8095

Other

OtherIEEE International Symposium on Information Theory, ISIT 2015
CountryHong Kong
CityHong Kong
Period6/14/156/19/15

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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