Uniform improvement of empirical likelihood for missing response problem

An empirical likelihood (EL) estimator was proposed by Qin and Zhang (2007) for improving the inverse probability weighting estimation in a missing response problem. The authors showed by simulation studies that the finite sample performance of EL, estimator is better than certain existing estimatiors and they also showed large sample results for the estimator. However, the empirical likelihood estimator does not have a uniformly smaller asymptotic variance than other existing estimators in general. We consider several modifications to the empirical likelihood estimator and show that the proposed estimator dominates the empirical likelihood estimator and several other existing estimators in terms of asymptotic efficiencies under missing at random. The proposed estimator also attains the minimum asymptotic variance among estimators having influence functions in a certain class and enjoys certain double robustness properties.