Estimation of Distribution Function and Quantiles Using the Model-calibrated Pseudo Empirical Likelihood Method

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 designunbiased irrespective of the working model and are also approximately modelunbiased 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.