- On a Conjecture of Bechhofer, Kiefer, and Sobel for the Levin-Robbins-Leu Binomial Subset Selection Procedures
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- Article comments:
- A brief version of this paper was delivered at the Sequential Analysis Workshop, Auburn, GA, July, 2007. A revised version has been accepted for publication in Sequential Analysis.
- Abstract:
- We state a general formula which provides a lower bound for the probability of various types of acceptable subset selection with the Levin-Robbins-Leu binomial subset selection procedure without elimination or recruitment. We prove the truth of a conjecture of Bechhofer, Kiefer, and Sobel for this procedure by applying the general lower bound. We also introduce a simple modification that allows sequential elimination of inferior populations and recruitment of superior populations. Numerical evidence indicates that the new procedure also obeys the general lower bound while reducing the expected number of observations and failures compared with non-adaptive methods.
- Subject Area:
- Statistical Theory and Methods
- Keywords:
- BKS conjecture, elimination and recruitment procedures, lower bound formulas, probability of acceptable selection, probability of correct selection, sequential selection, subset selection problem.
- Suggested Citation:
Cheng-Shiun Leu and Bruce Levin, "On a Conjecture of Bechhofer, Kiefer, and Sobel for the Levin-Robbins-Leu Binomial Subset Selection Procedures" (August 2007). Columbia University Biostatistics Technical Report Series. Working Paper 14.
http://biostats.bepress.com/columbiabiostat/papers/art14