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Sequential Analysis
Design Methods and Applications
Volume 27, 2008 - Issue 2
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Original Articles

On a Conjecture of Bechhofer, Kiefer, and Sobel for the Levin–Robbins–Leu Binomial Subset Selection Procedures

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Pages 106-125 | Received 22 Aug 2007, Accepted 28 Jan 2008, Published online: 19 May 2008

REFERENCES

  • Bechhofer , R. E. ( 1954 ). A Single-Sample Multiple Decision Procedure for Ranking Means of Normal Populations with Known Variances , Annals of Mathematical Statistics 25 : 16 – 39 .
  • Bechhofer , R. E. , Kiefer , J. , and Sobel , M. ( 1968 ). Sequential Identification and Ranking Procedures , Chicago : University of Chicago Press .
  • Chiu , W. K. ( 1974 ). A Generalized Selection Goal for a Sequential Ranking Procedure , Nanta Mathematica 7 : 42 – 46 .
  • Gupta , S. S. ( 1956 ). On a Decision Rule for a Problem in Ranking Means , Mimeograph Series 150, Institute of Statistics , Chapel Hill : University of North Carolina .
  • Gupta , S. S. ( 1965 ). On Some Multiple Decision (Selection and Ranking) Rules , Technometrics 7 : 225 – 245 .
  • Leu , C. S. and Levin , B. ( 1999a ). On the Probability of Correct Selection in the Levin–Robbins Sequential Elimination Procedure , Statistica Sinica 9 : 879 – 891 .
  • Leu , C. S. and Levin , B. ( 1999b ). Proof of a Lower Bound Formula for the Expected Reward in the Levin–Robbins Sequential Elimination Procedure , Sequential Analysis 18 : 81 – 105 .
  • Leu , C. S. and Levin , B. ( 2004 ). Selecting the Best Subset of b Out of c Coins with the Levin–Robbins Sequential Elimination Procedure: Proof of the Lower Bound Formula for the Probability of Correct Selection in the Case b = 2, c = 4, Technical Report #B-91, Department of Biostatistics, Columbia University, July 1, 2004, available at http://biostats.bepress.com/columbiabiostat/ .
  • Leu , C. S. and Levin , B. ( 2006 ). Proof of the Lower Bound Formula for the Probability of Correct Binomial Subset Selection with the Levin–Robbins–Leu Sequential Elimination and Recruitment Procedure in the Case b = 2, c = 4, Technical Report #B-98, Department of Biostatistics, Columbia University, December 15, 2006, available at http://biostats.bepress.com/columbiabiostat/ .
  • Leu , C. S. and Levin , B. ( 2008 ). A Generalization of the Levin-Robbins Procedure for Binomial Subset Selection and Recruitment Problems , Statistica Sinica , 18 : 203 – 218 .
  • Levin , B. ( 1984 ). On a Sequential Selection Procedure of Bechhofer, Kiefer, and Sobel , Statistics and Probability Letters 2 : 91 – 94 .
  • Levin , B. ( 2006 ). On Minimizing the Lower Bound for the Probability of θ-Acceptable Subset Selection, Technical Report #B-99, Department of Biostatistics, Columbia University, available at http://biostats.bepress.com/columbiabiostat/ .
  • Levin , B. and Robbins , H. ( 1981 ). Selecting the Highest Probability in Binomial or Multinomial Trials , Proceedings of National Academy of Sciences USA 78 : 4663 – 4666 .
  • Zybert , P. and Levin , B. ( 1987 ). Selecting the Highest of Three Binomial Probabilities , Proceedings of National Academy of Sciences USA 84 : 8180 – 8184 .
  • Recommended by Nitis Mukhopadhyay

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