Empirical likelihood for estimating equations with nonignorably missing data

We develop an empirical likelihood (EL) inference on parameters in generalized estimating equations with nonignorably missing data. We consider an exponential tilting model for the nonignorably missing mechanism, and propose modified estimating equations by imputing missing data through a kernel regression method. We establish some asymptotic properties of the maximum EL estimators of the unknown parameters under different scenarios. With the use of auxiliary information, the maximum EL estimators are statistically more efficient. Simulation studies are used to assess the finite sample performance of our proposed maximum EL estimators. We apply the proposed maximum EL estimators to investigate a data set on earnings obtained from the New York Social Indicators Survey.