Generalized Empirical Likelihood Inference for Single-index Models

Based on the generalized estimation equations(GEE) and the quadratic inference functions(QIF) methods,a bias-corrected generalized empirical likelihood was proposed to make statistical inference for the single-index model with longitudinal data. The maximum empirical likelihood estimator and the bias-corrected generalized empirical log-likelihood ratio statistics for the unknown index parameter in the model were obtained. It is proved that the maximum empirical likelihood estimator is asymptotically normal and the proposed statistics are asymptotically chi-square distributed under certain conditions,and hence they can be applied to construct the confidence region of the index parameter.