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Sequential Analysis
Design Methods and Applications
Volume 32, 2013 - Issue 4
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Original Articles

On an Inequality That Implies the Lower Bound Formula for the Probability of Correct Selection in the Levin-Robbins-Leu Family of Sequential Binomial Subset Selection Procedures

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Pages 404-427 | Received 21 Mar 2013, Accepted 15 Aug 2013, Published online: 14 Nov 2013

REFERENCES

  • Bechhofer , R. E. , Kiefer , J. , and Sobel , M. ( 1968 ). Sequential Identification and Ranking Procedures , Chicago : University of Chicago Press .
  • Gupta , S. S. ( 1956 ). On a Decision Rule for a Problem in Ranking Means, Mimeograph Series 150, Chapel Hill: Institute of Statistics, University of North Carolina.
  • Gupta , S. S. ( 1965 ). On Some Multiple Decision (Selection and Ranking) Rules , Technometrics 7 : 225 – 245 .
  • Hardy , G. H. , Littlewood , J. E. , and Pólya , G. ( 1934 ). Inequalities , Cambridge : Cambridge University Press .
  • Leu , C.-S. , Cheung , Y.-K. , and Levin , B. (2011). Subset Selection in Comparative Selection trials, in Recent Advances in Biostatistics: False Discovery, Survival Analysis, and Other Topics , Vol. 4, M. Bhattacharjee , S. K. Dhar and S. Subramanian , eds., pp. 271–288, London : World Scientific.
  • 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, New York, NY, 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, New York, NY, http://biostats.bepress.com/columbiabiostat/.
  • Leu , C.-S. and Levin , B. ( 2008a ). A Generalization of the Levin-Robbins Procedure for Binomial Subset Selection and Recruitment Problems , Statistica Sinica 18 : 203 – 218 .
  • Leu , C.-S. and Levin , B. ( 2008b ). On a Conjecture of Bechhofer, Kiefer, and Sobel for the Levin-Robbins-Leu Binomial Subset Selection Procedures , Sequential Analysis 27 : 106 – 125 .
  • Levin , B. and Leu , C.-S. ( 2007 ). A Comparison of Two Procedures to Select the Best Binomial Population with Sequential Elimination of Inferior Populations , Journal of Statistical Planning and Inference 137 : 245 – 263 .
  • Levin , B. and Leu , C.-S. ( 2013 ). On Two Lemmas Used to Establish a Key Inequality that Implies the Lower Bound Formula for the Probability of Correct Selection in the Levin-Robbins-Leu Family of Sequential Binomial Subset Selection Procedures, Technical Report #B-148, Department of Biostatistics, Columbia University, New York, NY, http://www.columbia.edu/ ∼bl6/appendices/.
  • 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 .
  • Marshall , A. W. , Olkin , I. , and Arnold , B. C. ( 2011 ). Inequalities: Theory of Majorization and Its Applications , second edition , New York : Springer .
  • Muirhead , R. F. ( 1903 ). Some Methods Applicable to Identities and Inequalities of Symmetric Algebraic Functions of n Letters , Proceedings of Edinburgh Mathematical Society 21 : 144 – 157 .
  • Wald , A. ( 1947 ). Sequential Analysis , New York : Wiley .
  • 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 Pinyuen Chen

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