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

TL;DR

This paper demonstrates strong positivity properties of a function that lead to a key inequality, providing a more direct proof of the lower bound formula for correct selection probability in sequential subset selection procedures.

Contribution

It introduces new positivity properties of a function that simplify and strengthen the proof of the lower bound in the Levin-Robbins-Leu family of procedures.

Findings

Establishes positivity properties of a specific function.

Provides a direct proof of the lower bound formula.

Enhances understanding of sequential subset selection probabilities.

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.