Generalized empirical likelihood inference in semiparametric regression model for longitudinal data

In this paper, we consider the semiparametric regression model for longitudinal data. Due to the correlation within groups, a generalized empirical log-likelihood ratio statistic for the unknown parameters in the model is suggested by introducing the working covariance matrix. It is proved that the proposed statistic is asymptotically standard chi-squared under some suitable conditions, and hence it can be used to construct the confidence regions of the parameters. A simulation study is conducted to compare the proposed method with the generalized least squares method in terms of coverage accuracy and average lengths of the confidence intervals. Supported by China Postdoctoral Science Foundation Funded Project (20080430633), Shanghai Postdoctoral Scientific Program (08R214121), the National Natural Science Foundation of China (10871013), the Research Fund for the Doctoral Program of Higher Education (20070005003), the Natural Science Foundation of Beijing (1072004) and the Basic Research and Frontier Technology Foundation of He’nan (072300410090)