Positivity of Cumulative Sums for Multi-Index Function Components Explains the Lower Bound Formula in the Levin-Robbins-Leu Family of Sequential Subset Selection Procedures

Abstract

We exhibit some strong positivity properties of a certain function which implies a key inequality that in turn implies the lower bound formula for the probability of correct selection in the Levin-Robbins-Leu family of sequential subset selection procedures for binary outcomes. These properties provide a more direct and comprehensive demonstration of the key inequality than was discussed in previous work.