On estimation of P(X> Y) based on judgement post stratification

Abstract

We propose an unbiased estimator for P(X> Y) and obtain an exact expression for its variance, based on judgement post stratification (JPS) sampling scheme. We then prove that the introduced estimator is consistent and establish its asymptotic normality. We show that the proposed estimator is at least as efficient asymptotically as its counterpart in simple random sampling (SRS), regardless of the quality of the rankings. For finite sample sizes, a Monte Carlo simulation study and a real data set are employed to show the preference of the JPS estimator to its SRS competitor in a wide range of settings. © 2017, Springer-Verlag GmbH Germany.