Empirical likelihood estimation for finite populations and the effective usage of auxiliary information

SUMMARY In finite population inference problems, auxiliary population information is often available. We show in this paper that the empirical likelihood method can be naturally applied to such problems to make effective use of the auxiliary information. We prove that the resulting estimates have smaller asymptotic variances than the usual estimates which do not use auxiliary information. A Bahadur-type representation for empirical likelihood sample quantiles is given. Simulation results show that the empirical likelihood estimates perform well among a number of competitors and are model robust.