Publication Cover
Sequential Analysis
Design Methods and Applications
Volume 23, 2004 - Issue 4
32
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Discussion on “Likelihood Ratio Identities and Their Applications to Sequential Analysis” by Tze L. Lai

Pages 509-515 | Received 01 Nov 2003, Published online: 23 Feb 2011

References

  • Armitage , P. 1950 . Sequential analysis with more than two alternative hypotheses, and its relation to discriminant function analysis . J. Roy. Statist. Soc., B , 12 : 137 – 144 .
  • Chernoff , H. 1961 . Sequential tests for the mean of a normal distribution . Proc. Fourth Berkeley Symp. Mathematical Statistics and Probability , 1 : 79 – 91 .
  • Chernoff , H. 1965 . Sequential tests for the mean of a normal distribution III (small t) . Ann. Math. Statist. , 36 : 28 – 54 .
  • Dragalin , V. 1993 . Optimality of generalized CUSUM procedure in quickest detection problem . Proceedings of Steklov Math. Inst.: Statistics and Control of Stochastic Processes. , 202 : 132 – 148 .
  • Dragalin , V. 1995 . Optimal sequential selection procedure . Commun. Statist. Theory Methods , 24 : 429 – 443 .
  • Dragalin , V. 1997 . The sequential change point problem . Econ. Qual. Control , 12 : 95 – 122 .
  • Dragalin , V. 1997 . The design and analysis of 2-CUSUM procedure . Commun. Statist. Sim. , 26 : 67 – 81 .
  • Dragalin , V. and Novikov , A.A. 1999 . Adaptive sequential tests for composite hypotheses . Rev. Appl. Ind. Math. , 6 : 387 – 398 . TVP Science Publ., Moscow
  • Dragalin , V. , Tartakovsky , A.A. and Veeravalli , V.V. 1999 . Multihypothesis sequential probability ratio tests—Part I: Asymptotic optimality . IEEE Trans. Inf. Theory , 45 : 2448 – 2461 . [CROSSREF]
  • Dragalin , V. , Tartakovsky , A.A. and Veeravalli , V.V. 2000 . Multihypothesis sequential probability ratio tests—Part II: Accurate asymptotic expansions for the expected sample size . IEEE Trans. Inf. Theory , 46 : 1366 – 1383 . [CROSSREF]
  • Kiefer , J. and Sacks , J. 1963 . Asymptotically optimal sequential inference and design . Ann. Math. Statist. , 34 : 705 – 750 .
  • Lai , T.L. 1981 . Asympotic optimality of invariant sequential probability ratio tests . Ann. Statist. , 9 : 318 – 333 .
  • Lai , T.L. 1988 . Nearly optimal sequential tests of composite hypotheses . Ann. Statist. , 16 : 856 – 886 .
  • Lorden , G. 1967 . Integrated risks of asymptotically Bayes sequential tests . Ann. Math. Statist. , 38 : 1399 – 1422 .
  • Lorden , G. 1972 . Likelihood ratio tests for sequential k-decision problems . Ann. Math. Statist. , 43 : 1412 – 1427 .
  • Lorden , G. 1977 . Nearly-optimal sequential tests for finitely many parameter values . Ann. Stat. , 5 : 1 – 21 .
  • Pavlov , I.V. 1988 . A sequential procedure for testing many composite hypotheses . Theory Prob. Appl. , 33 : 138 – 142 .
  • Pavlov , I.V. 1990 . A sequential procedure for testing composite hypotheses with applications to the Kiefer-Wess problem . Theory Prob. Appl. , 35 : 280 – 292 .
  • Schwarz , G. 1962 . Asymptotic shapes of Bayesian sequential testing regions . Ann. Math. Statist. , 33 : 224 – 236 .
  • Siegmund , D. and Venkatraman , E.S. 1995 . Using the generalized likelihood ratio statistic for sequential detection of a change-point . Ann. Statist. , 23 : 255 – 271 .
  • Sobel , M. and Wald , A. 1949 . A sequential decision procedure for choosing one of three hypotheses concerning the unknown mean of a normal distribution . Ann. Math. Statist. , 20 : 502 – 522 .
  • Recommended by: Nitis Mukhopadhyay

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.