Advertisement

Robust Hypothesis Testing with a Single Distance

  • Gökhan GülEmail author
Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 414)

Abstract

Design of a robust hypothesis test requires the simple hypotheses to be extended to the composite hypotheses via a suitable choice of uncertainty classes. The reader is referred to Sect.  2.2.2 for the fundamentals of robust hypothesis testing. In this chapter, minimax robust hypothesis testing is considered, where the uncertainty classes are built based on a single distance. From a single distance it is understood that the considered neighborhood classes accept only a single distance or a model.

Keywords

Robust Test Hellinger Distance Nominal Distribution Single Distance Uncertainty Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [AE84]
    J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis.   New York: J. Wiley, 1984.zbMATHGoogle Scholar
  2. [DJ94]
    A. G. Dabak and D. H. Johnson, “Geometrically based robust detection,” in Proceedings of the Conference on Information Sciences and Systems, Johns Hopkins University, Baltimore, MD, May 1994, pp. 73–77.Google Scholar
  3. [GZ13b]
    G. Gül and A. M. Zoubir, “Robust hypothesis testing for modeling errors,” in Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), Vancouver, Canada, May 2013, pp. 5514–5518.Google Scholar
  4. [GZ14b]
    G. Gül and A. M. Zoubir, “Robust hypothesis testing with squared Hellinger distance,” in Proc. 22nd European Signal Processing Conference (EUSIPCO), Lisbon, Portugal, September 2014, pp. 1083–1087.Google Scholar
  5. [Hub65]
    P. J. Huber, “A robust version of the probability ratio test,” Ann. Math. Statist., vol. 36, pp. 1753–1758, 1965.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [Joh81]
    P. Johnstone, “Tychonoff’s theorem without the axiom of choice,” Fundamenta Mathematicae, vol. 113, no. 1, pp. 21–35, 1981.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [Lev08]
    B. C. Levy, Principles of Signal Detection and Parameter Estimation, 1st ed.   Springer Publishing Company, Incorporated, 2008.CrossRefGoogle Scholar
  8. [Lev09]
    B. C. Levy, “Robust hypothesis testing with a relative entropy tolerance,” IEEE Transactions on Information Theory, vol. 55, no. 1, pp. 413–421, 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [LV06]
    F. Liese and I. Vajda, “On Divergences and Informations in Statistics and Information Theory”, IEEE Trans. Information Theory vol. 52, no. 10, pp. 4394–4412, 2006.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [Rud76]
    W. Rudin, Principles of Mathematical Analysis. International series in pure and applied mathematics. Paris: McGraw-Hill, 1976.zbMATHGoogle Scholar
  11. [Sio58]
    M. Sion, “On general minimax theorems.” Pacific Journal of Mathematics, vol. 8, no. 1, pp. 171–176, 1958.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [Tyc30]
    A. Tychonoff, “Über die topologische erweiterung von rumen,” Mathematische Annalen, vol. 102, no. 1, pp. 544–561, 1930.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [Wol96]
    E. Wolfstetter, “Stochastic dominance: Theory and applications,” 1996.Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institut für Nachrichtentechnik, Fachbereich Elektro- und Informationstechnik (ETIT)Technische Universität DarmstadtDarmstadtGermany

Personalised recommendations