Empirical likelihood inference for mean functionals with nonignorably missing response data

An empirical likelihood (EL) approach to inference on mean functionals with nonignorably missing response data is developed. The nonignorably missing mechanism is specified by an exponential tilting model. Several maximum EL estimators (MELEs) for the response mean functional are proposed under different scenarios. We systematically investigate asymptotic properties of the proposed MELEs for the response mean functional. With the use of auxiliary information, MELEs are statistically more efficient. Confidence intervals (CIs) for the response mean are constructed on the basis of the EL method and the normal approximation (NA) method. Simulation studies are presented to evaluate the finite sample performance of our proposed MELEs and CIs. A real earnings data from the New York Social Indicators Survey is used to illustrate our proposed EL method. Empirical results show that our proposed EL method is robust.