Multihypothesis sequential probability ratio tests - Part I: Asymptotic optimality

IEEE Transactions on Information Theory

Volumn 45, Issue 7, 1999, Pages 2448-2461

  Dragalin, Vladimir P ^b   Tartakovsky, Alexander G ^c   Veeravalli, Venugopal V ^a,d  

^a IEEE   (United States)

^b UNIVERSITY OF ROCHESTER   (United States)

^c UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^d Cornell University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC OPTIMALITY; INVARIANT SEQUENTIAL TESTS; MULTIALATERNATIVE SEQUENTIAL TESTS; ONE-SIDED SEQUENTIAL PROBABILITY RATIO TEST (SPRT); RENEWAL THEORY; SLIPPAGE PROBLEMS;

ERROR ANALYSIS; MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; PROBABILITY;

CORRELATION THEORY;

EID: 0033349954     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.796383     Document Type: Article

References (42)

1. P. Armitage, "Sequential analysis with more than two alternative hypotheses, and its relation to discriminant function analysis," J. Roy. Statist. Soc. B. vol. 12, pp. 137-144, 1950.
2. P. A. Bakut, I. A. Bolshakov, B. M. Gerasimov, A. A. Kuriksha, V. G. Repin, G. P. Tartakovsky, and V. V. Shirokov, Statistical Radar Theory, vol. 1, G. P. Tartakovsky, Ed. Moscow, USSR: Sov. Radio, 1963 (in Russian).
3. C. W. Baum and V. V. Veeravalli, "A sequential procedure for multihypothesis testing," IEEE Trans. Inform. Theory, vol. 40, pp. 1994-2007, Nov. 1994.
4. R. E. Bechhofer, J. Kiefer, and M. Sobel, Sequential Identification and Ranking Procedures (with special reference to Koopman-Darmois families). Chicago, IL: Univ. Chicago Press, 1968.
5. H. Chernoff, "Sequential design of experiments," Ann. Math. Statist., vol. 30, pp. 755-770, 1959.
6. _, Sequential Analysis and Optimal Design. Philadelphia, PA: SIAM, 1972.
7. Y.S. Chow and T. L. Lai, "Some one-sided theorems on the tail distribution of sample sums with applications to the last time and largest excess of boundary crossing," Trans. Amer. Math. Soc., vol. 208, pp. 51-72, 1975.
8. V. P. Dragalin, "Asymptotic solution of a problem of detecting a signal from k channels," Russ. Math. Surv., vol. 42, no. 3, pp. 213-214, 1987.
9. _, "Asymptotic solution of a problem of signal searching in multi-channel system," Mat. Issled (Acad, Sci. Moldova), vol. 109, pp. 15-35, 1989 (in Russian).
10. _, "Third-order asymptotics for a sequential selection procedure," Inst. Applications of Math, and Informatics, Milan, Italy, Tech. Rep., 1994;
11. to appear in Statist. Decisions (Special Issue in Honor of Professor Bechhofer).
12. V. P. Dragalin and A. A. Novikov, "Adaptive sequential tests for composite hypotheses," Inst. Applications of Math, and Informatics, Milan, Italy, Tech. Rep. 94.4, 1994.
13. V. P. Dragalin, A. G. Tartakovsky, and V. Veeravalli, "Multihypothesis sequential probability ratio tests, part II: Accurate asymptotic expansions for the expected sample size," IEEE Trans. Inform. Theory, submitted for publication.
14. B. Emlsee, S. K. Rogers, M. P. DeSimio, and R. A. Raines, "Complete automatic target recognition system for tactical forward-looking infrared images," Opt. Eng., vol. 36, pp. 2593-2603, Sept. 1997.
15. T. S. Ferguson, Mathematical Statistics: A Decision Theoretic Approach. New York/London: Academic, 1967.
16. M. M. Fishman, "Average duration of asymptotically optimal multialternative sequential procedure for recognition of processes," Sov. J. Commun. Technol. Electron., vol. 30, pp. 2541-2548, 1987.
17. K. S. Fu, Sequential Methods in Pattern Recognition and Learning. New York: Academic, 1968.
18. J. D. Gibbons, I. Olkin, and M. Sobel, Selecting and Ordering Populations: A New Statistical Methodology. New York: Wiley, 1977.
19. G. K. Golubev and R. Z. Khas'minskii, "Sequential testing for several signals in Gaussian white noise," Theory Prob. Appl., vol. 28, pp. 573-584, 1983.
20. A. Gut, Stopped Random Walks: Limit Theorems and Applications. New York: Springer-Verlag, 1988.
21. P. L. Hsu and H. Robbins, "Complete convergence and the law of large numbers," Proc. Nat. Acad. Sci. U.S.A., vol. 33, pp. 25-31, 1947.
22. J. Kiefer and J. Sacks, "Asymptotically optimal sequential inference and design," Ann. Math. Statist., vol. 34, pp. 705-750, 1963.
23. E. L. Lehmann, Testing Statistical Hypotheses. New York: Wiley, 1959.
24. T. L. Lai, "Asymptotic optimality of invariant sequential probability ratio test," Ann. Statist., vol. 9, pp. 318-333, 1981.
25. R. Sh. Liptser and A. N. Shiryaev, Statistics of Random Processes, vol. 1. New York: Springer-Verlag, 1977.
26. G. Lorden, "Nearly-optimal sequential tests for finitely many parameter values," Ann. Statist., vol. 5, pp. 1-21, 1977.
27. M. B. Marcus and P. Swerling, "Sequential detection in radar with multiple resolution elements," IRE Trans. Inform. Theory, vol. IT-8, pp. 237-245, 1962.
28. F. Mosteller, "A fc-sample slippage test for an extreme population," Ann. Math. Statist., vol. 19, pp. 58-65, 1948.
29. I. R. Savage and J. Sethuraman, "Stopping time of a rank-order sequential probability ratio test based on Lehmann alternatives," Ann. Math. Statist., vol. 37, pp. 1154-1160, 1966.
30. D. Siegmund, Sequential Analysis: Tests and Confidence Intervals. New York: Springer-Verlag, 1985.
31. Y. G. Sosulin and M. M. Fishman, Theory of Sequential Decisions and Its Applications. Moscow, USSR: Radio i Svyaz', 1985 (in Russian).
32. A. G. Tartakovskii, "Sequential testing of many simple hypotheses with dependent observations," Probl. Inform. Transm., vol. 24, pp. 299-309, 1988.
33. _, Sequential Methods in the Theory of Information Systems. Moscow, Russia: Radio i Svyaz', 1991 (in Russian).
34. _, "Minimax-invariant regret solution to the N-sample slippage problem," Math. Meth. Statist., vol. 6, no. 4, pp. 491-508, 1997.
35. _, "Asymptotically optimal sequential tests for nonhomogeneous processes," Sequential Anal., vol. 17, no. 1, pp. 33-61, 1998.
36. _, "Asymptotic optimality of certain multihypothesis sequential tests: non-i.i.d. case," Statist. Inference for Stochastic Processes, 1999.
37. V. V. Veeravalli and C. W. Baum, "Asymptotic efficiency of a sequential multihypothesis test," IEEE Trans. Inform. Theory, vol. 41, pp. 1994-1997, Nov. 1995.
38. _, "Hybrid acquisition of direct sequence CDMA signals," Int. J. Wireless Inform. Networks, vol. 3, pp. 55-65, Jan. 1996.
39. N. V. Verdenskaya and A. G. Tartakovskii, "Asymptotically optimal sequential testing of multiple hypotheses for nonhomogeneous Gaussian processes in an asymmetric situation," Theory Probab. Appl., vol. 36, pp. 536-547, 1991.
40. A. Wald, Sequential Analysis. New York: Wiley, 1947.
41. A. Wald and J. Wolfowitz, "Optimal character of the sequential probability ratio test," Ann. Math. Statist., vol. 19, pp. 326-339, 1948.
42. M. Woodroofe, Nonlinear Renewal Theory in Sequential Analysis. Philadelphia, PA: SIAM, 1982.