On the equivalence of f-Divergence balls and density bands in robust detection

Michael Faub, Abdelhak M. Zoubir, H. Vincent Poor

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

Abstract

The paper deals with minimax optimal statistical tests for two composite hypotheses, where each hypothesis is defined by a nonparametric uncertainty set of feasible distributions. It is shown that for every pair of uncertainty sets of the f-divergence-ball type, a pair of uncertainty sets of the density-band type can be constructed, which is equivalent in the sense that it admits the same pair of least favorable distributions. This result implies that robust tests under f-divergence-ball uncertainty, which are typically only minimax optimal for the single sample case, are also fixed sample size minimax optimal with respect to the equivalent density-band uncertainty sets.

Original languageEnglish (US)
Title of host publication2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4399-4403
Number of pages5
ISBN (Print)9781538646588
DOIs
StatePublished - Sep 10 2018
Event2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Calgary, Canada
Duration: Apr 15 2018Apr 20 2018

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2018-April
ISSN (Print)1520-6149

Other

Other2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018
CountryCanada
CityCalgary
Period4/15/184/20/18

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

Keywords

  • Density bands
  • Distributional uncertainty
  • Divergence
  • Hypothesis testing
  • Robust detection

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  • Cite this

    Faub, M., Zoubir, A. M., & Poor, H. V. (2018). On the equivalence of f-Divergence balls and density bands in robust detection. In 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings (pp. 4399-4403). [8462520] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2018-April). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2018.8462520