On lattice event probabilities for Levin-Robbins-Leu subset selection procedures

ABSTRACT

The Levin-Robbins-Leu (LRL) family of sequential subset selectionprocedures admits of a simple formula that provides a lower bound for the probability of various types of subset selection events. Here we demonstrate that a corresponding lower bound formula holds for lattice events when using the nonadaptive family member with binary outcomes. Lattice events are more general than the type of events that we previously considered in demonstrating that the nonadaptive LRL procedure selects “acceptable” subsets with an arbitrarily large prespecified probability irrespective of the true population parameters. Interestingly, the proof of the lower bound formula for lattice events that we present here simplifies the methods previously used and sheds additional light on why the lower bound formula holds. As for acceptable subset selection, we conjecture that the other LRL family members, which allow for adaptive elimination of inferior candidates and/or recruitment of superior candidates, obey the same lower bound formulas for lattice events.

KEYWORDS:

• BKS conjecture
• elimination and recruitment procedures
• lattice events
• Levin-Robbins-Leu family
• lower bound formulas
• probability of acceptable selection
• probability of correct selection
• sequential selection
• subset selection

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62F07
• 62F35
• 62L10
• 74Q20