Abstract: We use the model-calibrated pseudo empirical likelihood method to construct estimators for the finite population distribution function. Under an assumed superpopulation working model, the proposed estimators have minimum model expectation of asymptotic design-based variance among a class of estimators and therefore are optimal in that class. The estimators are asymptotically design-unbiased irrespective of the working model and are also approximately model-unbiased under the model. They share the design-based asymptotic efficiency with that of a generalized regression estimator but, unlike the latter, the estimators are genuine distribution functions. Quantile estimation through direct inversion and using a model-calibrated difference estimator are studied, and their asymptotic efficiency is investigated through Bahadur representations. Variance estimation and confidence intervals for the distribution function are also addressed. Results of a limited simulation study regarding the finite sample performance of proposed estimators are reported.
Key words and phrases: Auxiliary information, Bahadur representation, design consistency, finite population, model-assisted approach, model calibration, variance estimation.