Advertisement

Robust Hypothesis Testing with Multiple Distances

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

Abstract

As mentioned in the previous chapter, a minimax robust test can be designed based on a suitable choice of a distance between probability measures, which is most likely decided for, depending on the application. Instead of searching for a distance and performing a tedious design procedure, it is probably most convenient to choose a simple parameter, which accounts for the distance. In this way, the designer has the flexibility to choose both the degree of robustness as well as the type of the distance with only setting a few parameters.

Keywords

Probability Measure Likelihood Ratio Test Robust Test Hellinger Distance Total Variation Distance 
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. [BNO03]
    D. Bertsekas, A. Nedić, and A. Ozdaglar, Convex Analysis and Optimization, ser. Athena Scientific optimization and computation series.   Athena Scientific, 2003.zbMATHGoogle Scholar
  2. [CiA10]
    A. Cichocki and S. ichi Amari, “Families of alpha- beta- and gamma- divergences: Flexible and robust measures of similarities,” Entropy, vol. 12, no. 6, pp. 1532–1568, 2010.Google Scholar
  3. [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
  4. [GZ14a]
    G. Gül and A. M. Zoubir, “Robust hypothesis testing with composite distances,” in Proc. IEEE Workshop on Statistical Signal Processing, Gold Coast, Australia, June 2014, pp. 432–435.Google Scholar
  5. [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
  6. [Hub65]
    P. J. Huber, “A robust version of the probability ratio test,” Ann. Math. Statist., vol. 36, pp. 1753–1758, 1965.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [HS68]
    P. J. Huber, “Robust confidence limits,” Z. Wahrcheinlichkeitstheorie verw. Gebiete, vol. 10, pp. 269–278, 1968.Google Scholar
  8. [Lev08]
    B. C. Levy, Principles of Signal Detection and Parameter Estimation, 1st ed.   Springer Publishing Company, Incorporated, 2008.CrossRefGoogle Scholar
  9. [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
  10. [ZS07]
    Q. Zhao and B. M. Sadler, “A survey of dynamic spectrum access,” IEEE Signal Processing Magazine, vol. 24, no. 3, pp. 79–89, May 2007.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