College of Applied Sciences,Beijing University of Technology School of Finance and Statistics,East China Normal University College of Mathematics and Science,Luoyang Normal University

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.