Proof of a Key Inequality for Lattice Event Probabilities with Equal Odds. Issue 4 (2nd October 2022)

• Record Type: Journal Article
• Authors: Levin, Bruce; Leu, Cheng-Shiun
• Is Part Of: Sequential analysis. Volume 41:Issue 4(2022)
• Page Start: 451
• Page End: 491
• Publication Date: 2022-10-02
• Subjects: Adaptive subset selection -- Elimination and recruitment procedures -- Lattice events -- Lower-bound formulas -- Positive cusum property -- Probability of correct selection -- Sequential selection -- Subset selection; 62F07 -- 62F35 -- 62L10 -- 74Q20; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2022.2129689
• Languages: English
• ISSNs: 0747-4946

Abstract

Abstract: Levin and Leu (2021 ) introduced some key inequalities that underlie the lower bound formula for the probability of lattice events when using adaptive members of the Levin-Robbins-Leu family of sequential subset selection procedures for binary outcomes. Here we provide a rigorous proof of the key inequality for each adaptive procedure in the special case of equal odds parameters. We also provide some further insight into why the key inequality holds for arbitrary odds parameters and we present a complete proof in that case for a simple yet non-trivial prototype example. Two errata in the abovementioned publication are also corrected herein.