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).

Keywords:

• Adaptive subset selection
• elimination and recruitment procedures
• lower-bound formulas
• multiple-index CUSUMs
• probability of correct selection
• sequential selection
• standardized Muirhead ratios
• subset selection

SUBJECT CLASSIFICATIONS:

• 62F07
• 62F35
• 62L10
• 74Q20

ACKNOWLEDGMENT

We thank the Editors and referees for their generous efforts on our behalf.

DISCLOSURE

The authors have no conflicts of interest to report.