Empirical Likelihood Confidence Regions of the Parametersin Single-Index Models for Longitudinal Data

In this paper, the single-index model for longitudinal data is considered, three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested to accommodate the independence of different subjects for longitudinal data. It is proved that the proposed statistics are asymptotically chi-square distribution under some suitable conditions, and hence they can be used to construct the confidence regions of the parameters. Furthermore, it is shown that the bias corrected empirical log-likelihood ratio shares some desired features. A simulation study is conducted to illustrate our methods.