Empirical Likelihood for Generalized Linear Models with Longitudinal Data

Generalized linear models are usually adopted to model the discrete or nonnegative responses. In this paper, empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigated. Under some mild conditions, the consistency and asymptotic normality of the maximum empirical likelihood estimator are established, and the asymptotic χ2 distribution of the empirical log-likelihood ratio is also obtained. Compared with the existing results, the new conditions are more weak and easy to verify. Some simulations are presented to illustrate these asymptotic properties.