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 that 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 Levin and Leu (2013a).