On Bounded Length Sequential Confidence Intervals Based on One-Sample Rank Order Statistics

Abstract

The problem of obtaining sequential confidence intervals for the median of an unknown symmetric distributon based on a general class of one-sample rank-order statistics is considered. It is shown that the usual one-sample rank-order statistic possesses the martingale or sub-martingale property according as the parent distribution is symmetric about the origin or not. Certain asymptotic almost sure convergence results (with specified order of convergence) for a class of rank-order processes and the empirical distribution are derived, and these are then utilized for the study of the properties of the proposed procedures.