Abstract
We introduce a family of sequential selection and recruitment procedures for the subset identification problem in binomial populations. We demonstrate the general validity of a simple formula providing a lower bound for the probability of correct identification in a version of the family without sequential elimination or recruitment. A new application of the noncentral hypergeometric distribution is revealed. A similar theorem is conjectured to hold for the more efficient version which employs sequential elimination or recruitment.
Keywords: lower bound formula, probability of correct selection, recruitment, selection, sequential identification.
Disciplines
Statistical Methodology | Statistical Theory
Suggested Citation
Leu, Cheng-Shiun and Levin, Bruce, "A Generalization of the Levin-Robbins Procedure for Binomial Subset Selection and Recruitment Problems" (April 2006). Columbia University Biostatistics Technical Report Series. Working Paper 2.
http://biostats.bepress.com/columbiabiostat/art2
Proof of the lower bound formula in the case b=2, c=4, and any r.
Tech Report B-92.pdf (122 kB)
Formulas for the exact probability of correct selection in the case b=2, c=3 and b=2, c=4 for r=1
Comments
This paper has been accepted for publication in Statistica Sinica.