Skip to main content
SpringerLink
Log in

Robust Hypothesis Testing with Repeated Observations

  • Chapter
  • First Online:
Robust and Distributed Hypothesis Testing

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 414))

  • 978 Accesses

Abstract

Multiple observations are available in many applications, and are used to improve the detection or estimation accuracy by exploiting the information in data samples. In this chapter, the robust tests treated in Chaps. 3–4 are extended to multiple, fixed as well as variable (sequential), sample size tests. In both cases, it is both theoretically proven and shown with simulations whether the robust tests preserve their minimax properties.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Notes

  1. 1.

    In Chap. 7 analytical properties of the ROC curves can be found.

References

  1. H. Cramér, “Sur un nouveau théorème-limite de la théorie des probabilités,” Actualités Scientifiques et Industrielles, no. 736:5-23, 1938.

    MATH  Google Scholar 

  2. 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. W. Feller, An Introduction to Probability Theory and Its Applications. Wiley, January 1968, vol. 1.

    Google Scholar 

  4. P. J. R. Frank R. Hampel, Elvezio M. Ronchetti and W. A. Stahel, Robust Statistics - The Approach Based on Influence Functions. Wiley, 1986.

    Google Scholar 

  5. P. J. Huber, “A robust version of the probability ratio test,” Ann. Math. Statist., vol. 36, pp. 1753–1758, 1965.

    Article  MathSciNet  MATH  Google Scholar 

  6. P. J. Huber, Robust statistics. Wiley New York, 1981.

    Google Scholar 

  7. P. J. Huber, “Robust confidence limits,” Z. Wahrcheinlichkeitstheorie verw. Gebiete, vol. 10, pp. 269–278, 1968.

    Google Scholar 

  8. K. D. Kharin, A., “Robust sequential testing of hypothesis on discrete probability distributions,” Austrian Journal of Statistics, vol. 34, no. 2, pp. 153–162, 2005.

    Google Scholar 

  9. B. C. Levy, Principles of Signal Detection and Parameter Estimation, 1st ed. Springer Publishing Company, Incorporated, 2008.

    Book  Google Scholar 

  10. S. Lyu and H. Farid, “Detecting hidden messages using higher-order statistics and support vector machines,” in In 5th International Workshop on Information Hiding. Springer-Verlag, 2002, pp. 340–354.

    Google Scholar 

  11. Moving and stationary target acquisition and recognition (MSTAR) database. [Online] https://www.sdms.afrl.af.mil/index.php?collection=mstar&page=targets

  12. Personal web-page of Hany Farid. [Online]. Available: http://www.cs.dartmouth.edu/farid/

  13. P. X. Quang, “Minimax tests and the Neyman-Pearson lemma for capacities,” Ann. Statistics, vol. 1, pp. 251–263, 1973.

    MathSciNet  MATH  Google Scholar 

  14. P. X. Quang, “Robust sequential testing,” Annals of Statistics, vol. 13, no. 2, pp. 638–649, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  15. D. Vats, V. Monga, U. Srinivas, and J. Moura, “Scalable robust hypothesis tests using graphical models,” in Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on, May 2011, pp. 3612–3615.

    Google Scholar 

  16. A. Wald, “Sequential tests of statistical hypotheses,” The Annals of Mathematical Statistics, vol. 16, no. 2, pp. 117–186, 06 1945.

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Gökhan Gül

Authors
  1. Gökhan Gül
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gökhan Gül .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Gül, G. (2017). Robust Hypothesis Testing with Repeated Observations. In: Robust and Distributed Hypothesis Testing. Lecture Notes in Electrical Engineering, vol 414. Springer, Cham. https://doi.org/10.1007/978-3-319-49286-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-49286-5_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-49285-8

  • Online ISBN: 978-3-319-49286-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation