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Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 393095, 15 pages
http://dx.doi.org/10.1155/2010/393095
Research Article

Hypothesis Designs for Three-Hypothesis Test Problems

School of Finance and Statistics, East China Normal University, No. 500 Dongchuan Road, Shanghai 200241, China

Received 25 January 2010; Accepted 18 March 2010

Academic Editor: Ming Li

Copyright © 2010 Yan Li and Xiaolong Pu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. S. Fu, Sequential Methods in Pattern Recognition and Learning, Academic Press, New York, NY, USA, 1968.
  2. W. E. Waters, “Sequential sampling in forest insect surveys,” Forest Science, vol. 1, pp. 68–79, 1955.
  3. B. Lye and R. N. Story, “Spatial dispersion and sequential sampling plan of the southern green stink bug on fresh market tomatoes,” Environmental Entomology, vol. 18, no. 1, pp. 139–144, 1989.
  4. T. McMillen and P. Holmes, “The dynamics of choice among multiple alternatives,” Journal of Mathematical Psychology, vol. 50, no. 1, pp. 30–57, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J. J. Bussgang, “Sequential methods in radar detection,” Proceedings of the IEEE, vol. 58, no. 5, pp. 731–743, 1970.
  6. E. Grossi and M. Lops, “Sequential along-track integration for early detection of moving targets,” IEEE Transactions on Signal Processing, vol. 56, no. 8, pp. 3969–3982, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. N. A. Goodman, P. R. Venkata, and M. A. Neifeld, “Adaptive waveform design and sequential hypothesis testing for target recognition with active sensors,” IEEE Journal on Selected Topics in Signal Processing, vol. 1, no. 1, pp. 105–113, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. S. L. Anderson, “A simple method of comparing the breaking loads of two yarns,” Textile Institute, vol. 45, pp. 472–479, 1954.
  9. C. Liteanu and I. Rica, Statistical Theory and Methodology of Trace Analysis, Halsted, New York, NY, USA, 1980.
  10. A. G. Tartakovsky, B. L. Rozovskii, R. B. Blažek, and H. Kim, “Detection of intrusions in information systems by sequential change-point methods,” Statistical Methodology, vol. 3, no. 3, pp. 252–293, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. G. B. Wetherill and K. D. Glazebrook, Sequential Methods in Statistics, Monographs on Statistics and Applied Probability, Chapman & Hall, London, UK, 3rd edition, 1986. View at MathSciNet
  12. T.-H. Chen, C.-Y. Chen, H.-C. P. Yang, and C.-W. Chen, “A mathematical tool for inference in logistic regression with small-sized data sets: a practical application on ISW-ridge relationships,” Mathematical Problems in Engineering, vol. 2008, Article ID 186372, 12 pages, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. T. F. Oliveira, R. B. Miserda, and F. R. Cunha, “Dynamical simulation and statistical analysis of velocity fluctuations of a turbulent flow behind a cube,” Mathematical Problems in Engineering, vol. 2007, Article ID 24627, 28 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  14. M. Li and W. Zhao, “Variance bound of ACF estimation of one block of fGn with LRD,” Mathematical Problems in Engineering, vol. 2010, Article ID 560429, 14 pages, 2010. View at Publisher · View at Google Scholar
  15. M. Li, W.-S. Chen, and L. Han, “Correlation matching method for the weak stationarity test of LRD traffic,” Telecommunication Systems, vol. 43, no. 3-4, pp. 181–195, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. E. G. Bakhoum and C. Toma, “Relativistic short range phenomena and space-time aspects of pulse measurements,” Mathematical Problems in Engineering, vol. 2008, Article ID 410156, 20 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. C. Cattani, “Harmonic wavelet approximation of random, fractal and high frequency signals,” Telecommunication Systems, vol. 43, no. 3-4, pp. 207–217, 2010.
  18. C. Cattani and A. Kudreyko, “Application of periodized harmonic wavelets towards solution of eigenvalue problems for integral equations,” Mathematical Problems in Engineering, vol. 2010, Article ID 570136, 8 pages, 2010. View at Publisher · View at Google Scholar
  19. P. Armitage, “Sequential analysis with more than two alternative hypotheses, and its relation to discriminant function analysis,” Journal of the Royal Statistical Society. Series B, vol. 12, pp. 137–144, 1950. View at Zentralblatt MATH · View at MathSciNet
  20. M. E. Payton and L. J. Young, “A sequential procedure for deciding among three hypotheses,” Sequential Analysis, vol. 13, no. 4, pp. 277–300, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. M. E. Payton and L. J. Young, “A sequential procedure to test three values of a binomial parameter,” Metrika, vol. 49, no. 1, pp. 41–52, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. V. P. Dragalin, A. G. Tartakovsky, and V. V. Veeravalli, “Multihypothesis sequential probability ratio tests. I. Asymptotic optimality,” IEEE Transactions on Information Theory, vol. 45, no. 7, pp. 2448–2461, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. V. P. Dragalin, A. G. Tartakovsky, and V. V. Veeravalli, “Multihypothesis sequential probability ratio tests. II. Accurate asymptotic expansions for the expected sample size,” IEEE Transactions on Information Theory, vol. 46, no. 4, pp. 1366–1383, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. Y. Li and X. L. Pu, “A method on designing three-hypothesis test problems,” to appear in Communications in Statistics—Simulation and Computation.
  25. M. R. Reynolds Jr. and Z. G. Stoumbos, “The SPRT chart for monitoring a proportion,” IIE Transactions, vol. 30, no. 6, pp. 545–561, 1998. View at Scopus
  26. Y. Li, X. L. Pu, and F. Tsung, “Adaptive charting schemes based on double sequential probability ratio tests,” Quality and Reliability Engineering International, vol. 25, no. 1, pp. 21–39, 2009. View at Publisher · View at Google Scholar · View at Scopus