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.
Statistical Methodology | Statistical Theory
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.