Universal and composite hypothesis testing via mismatched divergence

IEEE Transactions on Information Theory

Volumn 57, Issue 3, 2011, Pages 1587-1603

  Unnikrishnan, Jayakrishnan ^a   Huang, Dayu ^b   Meyn, Sean P ^b   Surana, Amit ^c   Veeravalli, Venugopal V ^b  

^a EPFL   (Switzerland)

^b United States of America   (United States)

^c UNITED TECHNOLOGIES RESEARCH CENTER   (United States)

Author keywords

Generalized likelihood ratio test; hypothesis testing; KullbackLeibler (K L) information; online detection

Indexed keywords

ASYMPTOTIC PERFORMANCE; ASYMPTOTIC VARIANCE; COMPOSITE HYPOTHESIS TESTING; DIMENSIONAL PARAMETERS; EMPIRICAL DISTRIBUTIONS; ERROR EXPONENT; EXPONENTIAL FAMILY; FINITE SAMPLES; GENERALIZED LIKELIHOOD RATIO TEST; GENERALIZED LIKELIHOOD-RATIO TESTS; HYPOTHESIS TESTING; KULLBACK-LEIBLER; KULLBACK-LEIBLER INFORMATION; LARGE ALPHABETS; NULL HYPOTHESIS; ON-LINE DETECTION; PARAMETRIC FAMILY; PARTICULAR DISTRIBUTION; UNIVERSAL TEST;

ASYMPTOTIC ANALYSIS; PROBABILITY; SAMPLING; STATISTICS;

STATISTICAL TESTS;

EID: 79951922225     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2104670     Document Type: Article

References (24)

1. D. Huang, J. Unnikrishnan, S. P. Meyn, V. Veeravalli, and A. Surana, "Statistical SVMs for robust detection, supervised learning, and universal classification," in Proc. IEEE Information Theory Workshop on Networking and Information Theory, Volos, Greece, 2009, pp. 62-66.
2. W. Hoeffding, "Asymptotically optimal tests for multinomial distributions," Ann. Math. Statist., vol. 36, pp. 369-408, 1965.
3. O. Zeitouni, J. Ziv, and N. Merhav, "When is the generalized likelihood ratio test optimal?," IEEE Trans. Inf. Theory, vol. 38, no. 5, pp. 1597-1602, Sep. 1992.
4. E. Levitan and N. Merhav, "A competitive Neyman-Pearson approach to universal hypothesis testing with applications," IEEE Trans. Inf. Theory, vol. 48, no. 8, pp. 2215-2229, Aug. 2002. (Pubitemid 35017062)
5. A. Lapidoth, "Mismatched decoding and the multiple-access channel," IEEE Trans. Inf. Theory, vol. 42, no. 5, pp. 1439-1452, Sep. 1996. (Pubitemid 126768893)
6. E. Abbe, M. Medard, S. P. Meyn, and L. Zheng, "Finding the best mismatched detector for channel coding and hypothesis testing," in Proc. Information Theory and Applications Workshop, Feb. 2, 2007, pp. 284-288.
7. I. Csiszár and P. C. Shields, "Information theory and statistics: A tutorial," Found. Trends Commun. Inf. Theory, vol. 1, no. 4, 2004.
8. C. Pandit, S. P. Meyn, and V. V. Veeravalli, "Asymptotic robust Neyman-Pearson hypothesis testing based on moment classes," in Proc. IEEE Int. Symp. Information Theory, Chicago, IL, 2004, pp. 220-220.
9. C. Pandit and S. P. Meyn, "Worst-case large-deviations with application to queueing and information theory," Stoch. Proc. Applns., vol. 116, pp. 724-756, May 2006. (Pubitemid 44262037)
10. M. Donsker and S. Varadhan, "Asymptotic evaluation of certain Markov process expectations for large time. I. II," Comm. Pure Appl. Math., vol. 28, pp. 1-47, 1975.
11. X. Nguyen, M. J.Wainwright, and M. I. Jordan, "Estimating divergence functionals and the likelihood ratio by convex risk minimization," IEEE Trans. Inf. Theory, vol. 56, no. 11, pp. 5847-5861, Nov. 2010.
12. B. Clarke and A. R. Barron, Information Theoretic Asymptotics of Bayes' Methods, Dept. Statistics, Univ., Illinois Urbana-Champaign, 1989, Tech. Rep. 26.
13. B. S. Clarke and A. R. Barron, "Information-theoretic asymptotics of Bayes methods," IEEE Trans. Inf. Theory, vol. 36, no. 3, pp. 453-471, May 1990.
14. S. S. Wilks, "The large-sample distribution of the likelihood ratio for testing composite hypotheses," Ann. Math. Statist., vol. 9, pp. 60-62, 1938.
15. M. Iltis, "Sharp asymptotics of large deviations in ," J. Theoret. Probab., vol. 8, no. 3, pp. 501-522, 1995.
16. P. Harremoës, "Testing goodness-of-fit via rate distortion," in Proc. IEEE Information Theory Workshop on Networking and Information Theory, Volos, Greece, Jun. 2009, pp. 17-21.
17. O. Zeitouni and M. Gutman, "On universal hypotheses testing via large deviations," IEEE Trans. Inf. Theory, vol. 37, no. 2, pp. 285-290, Mar. 1991.
18. O. Zeitouni and M. Gutman, "Correction to: "On universal hypotheses testing via large deviations"," IEEE Trans. Inf. Theory, vol. 37, no. 3, pt. 1, p. 698, May 1991.
19. E. Zhao, M. C. Fu, and S. I. Marcus, "Solving continuous-state POMDPs via density projection," IEEE Trans. Autom. Control, vol. 55, no. 5, pp. 1101-1116, May 2010.
20. J. Unnikrishnan, "Decision-Making Under Statistical Uncertainty," Ph.D. dissertation, Univ. Illinois Urbana-Champaign, Urbana, IL, 2010.
21. J. Unnikrishnan, S. P. Meyn, and V. V. Veeravalli, "On thresholds for robust goodness-of-fit tests,," in IEEE Information Theory Workshop (ITW), Sep. 2010, pp. 1-4.
22. D. Huang and S. P. Meyn, "Feature extraction for universal hypothesis testing via rank-constrained optimization," in Proc. IEEE Int. Symp. Information Theory Proceedings (ISIT), Jun. 2010, pp. 1618-1622.
23. S. P. Meyn, A. Surana, Y. Lin, and S. Narayanan, "Anomaly detection using projective Markov models in a distributed sensor network," in Proc. 48th IEEE Conf. Decision and Control, Shanghai, China, Dec. 2009, pp. 4662-4669.
24. P. Billingsley, Convergence of Probability Measures. Hoboken, NJ: Wiley, 1968.