A key inequality for lower bound formulas for lattice event probabilities. Issue 4 (2nd October 2021)

• Record Type: Journal Article
• Authors: Levin, Bruce; Leu, Cheng-Shiun
• Is Part Of: Sequential analysis. Volume 40:Issue 4(2021)
• Page Start: 554
• Page End: 574
• Publication Date: 2021-10-02
• Subjects: Adaptive subset selection -- elimination and recruitment procedures -- lattice events -- lower-bound formulas -- multiple-index cusums -- probability of correct selection -- sequential selection -- standardized Muirhead ratios -- subset selection; 62F07 -- 62F35 -- 62L10 -- 74Q20; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2021.2010417
• Languages: English
• ISSNs: 0747-4946

Abstract

Abstract: We introduce and discuss some key inequalities that underlie the lower bound formula for the probability of lattice events in the Levin-Robbins-Leu family of sequential subset selection procedures for binary outcomes. The present work combines the notion of lattice events —as previously discussed for the nonadaptive member of the family—with the positive cumulative sum property for the adaptive members—as previously discussed for the special lattice event of correct selection, thereby extending the key inequality to its broadest scope.