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Composite Hypothesis Testing

  • Bernard C. Levy
Chapter

Keywords

False Alarm Detection Problem Invariant Test Asymptotic Optimality Composite Hypothesis 
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.

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References

  1. 1.
    E. L. Lehmann, Elements of Large-Sample Theory. New York: Springer Verlag, 1999.Google Scholar
  2. 2.
    S. M. Kay and J. R. Gabriel, “An invariance property of the generalized likelihood ratio test,” IEEE Signal Proc. Letters, vol. 10, pp. 352–355, Dec. 2003.Google Scholar
  3. 3.
    S. Karlin and H. Rubin, “The theory of decision procedures for distributions with monotone likelihood ratios,” Annals Math. Statistics, vol. 27, pp. 272–299, 1956.CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    C. W. Helstrom, Elements of Signal Detection & Estimation. Upper Saddle River, NJ: Prentice-Hall, 1995.MATHGoogle Scholar
  5. 5.
    S. Bose and A. O. Steinhardt, “Optimum array detector for a weak signal in unknown noise,” IEEE Trans. Aerospace Electronic Systems, vol. 32, pp. 911–922, July 1996.CrossRefGoogle Scholar
  6. 6.
    L. L. Scharf, Statistical Signal Processing: Detection, Estimation and Time Series Analysis. Reading, MA: Addison Wesley, 1991.MATHGoogle Scholar
  7. 7.
    A. J. Laub, Matrix Analysis for Scientists and Engineers. Philadelphia, PA: Soc. for Industrial and Applied Math., 2005.CrossRefMATHGoogle Scholar
  8. 8.
    H. L. Van Trees, Optimum Array Processing. New York: J. Wiley & Sons, 2002.CrossRefGoogle Scholar
  9. 9.
    F. Nicolls and G. de Jager, “Uniformly most powerful cyclic permutation invariant detection for discrete-time signals,” in Proc. 2001 IEEE Internat. Conf. on Acoustics, Speech, Signal Proc. (ICASSP ’01), vol. 5, (Salt Lake City, UT), pp. 3165–3168, May 2001.Google Scholar
  10. 10.
    A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, Fourth Edition. New York: McGraw Hill, 2002.Google Scholar
  11. 11.
    H. Chernoff, “On the distribution of the likelihood ratio,” Annals Math. Statist., vol. 25, pp. 573–578, Sept. 1954.CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    W. Hoeffding, “Asymptotically optimal tests for multinomial distributions,” Annals Math. Statistics, vol. 36, pp. 369–401, Apr. 1965.CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    F. den Hollander, Large Deviations. Providence, RI: American Mathematical Soc., 2000.MATHGoogle Scholar
  14. 14.
    A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Second Edition. New York: Springer Verlag, 1998.Google Scholar
  15. 15.
    O. Zeitouni and M. Gutman, “On universal hypothesis testing with large deviations,” IEEE Trans. Informat. Theory, vol. 37, pp. 285–290, Mar. 1991.CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    O. Zeitouni, J. Ziv, and N. Merhav, “When is the generalized likelihood ratio test optimal?,” IEEE Trans. Informat. Theory, vol. 38, pp. 1597–1602, 1992.CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    D. G. Herr, “Asymptotically optimal tests for multivariate normal distributions,” Annals Math. Statistics, vol. 38, pp. 1829–1844, Dec. 1967.CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    B. Efron and D. Truax, “Large deviations theory in exponential families,” Annals Math. Statistics, vol. 39, pp. 1402–1424, Oct. 1968.MATHMathSciNetGoogle Scholar
  19. 19.
    W. C. M. Kallenberg, Asymptotic Optimality of Likelihood Ratio Tests in Exponential Families. Amsterdam: Mathematical Centre, 1978.MATHGoogle Scholar
  20. 20.
    S. Kourouklis, “A large deviations result for the likelihood ratio statistic in exponential families,” Annals of Statistics, vol. 12, pp. 1510–1521, Dec. 1984.CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    L. D. Brown, “Non-local asymptotic optimality of appropriate likelihood ratio tests,” Annals Math. Statistics, vol. 42, pp. 1206–1240, 1971.CrossRefMATHGoogle Scholar
  22. 22.
    P. J. Bickel and K. A. Doksum, Mathematical Statistics: Basic Ideas and Selected Topics, Second Edition.Google Scholar
  23. 23.
    S. M. Kay, Fundamentals of Statistical Signal Processing: Detection Theory. Prentice-Hall, 1998.Google Scholar
  24. 24.
    M. Feder and N. Merhav, “Universal composite hypothesis testing: a composite minimax approach,” IEEE Trans. Informat. Theory, vol. 48, pp. 1504–1517, June 2002.CrossRefMATHMathSciNetGoogle Scholar
  25. 25.
    E. Levitan and N. Merhav, “A competitive Neyman-Pearson approach to universal hypothesis testing with applications,” IEEE Trans. Informat. Theory, vol. 48, pp. 2215–2229, Aug. 2002.CrossRefMATHMathSciNetGoogle Scholar
  26. 26.
    A. A. Tadaion, M. Derakhtian, S. Gazor, M. M. Nayebi, and M. A. Aref, “Signal activity detection of phase-shift keying signals,” IEEE Trans. Commun., vol. 54, pp. 1439–1445, Aug. 2006.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Bernard C. Levy
    • 1
  1. 1.University of CaliforniaDavisUSA

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