Statistica Sinica 9(1999), 879-891

ON THE PROBABILITY OF CORRECT SELECTION IN THE

LEVIN-ROBBINS SEQUENTIAL ELIMINATION PROCEDURE

Cheng-Shiun Leu$^{*\dagger}$ and Bruce Levin$^{\dagger}$

$^*$New York State Psychiatric Institute and $^{\dagger}$Columbia University

Abstract: We prove the general validity of a formula conjectured by Levin and Robbins (1981) to give a lower bound for the probability of correct selection in a sequential elimination procedure designed to identify the best of $c$ binomial populations. The formula is elementary to calculate and simplifies the design of the selection procedure.

Key words and phrases: Lower bound formula, probability of correct selection, sequential elimination procedure.