Penalized empirical likelihood for high-dimensional generalized linear models with longitudinal data

In this paper, we consider the application of penalized empirical likelihood to the high-dimensional generalized linear models with longitudinal data. Under regular conditions, it is shown that the penalized empirical likelihood has the oracle property. That is, with probability converging to one, the penalized empirical likelihood identifies the true model and estimates the nonzero coefficients as efficiently as if the sparsity of the true model was known in advance. Also, we find the asymptotic distribution of the penalized empirical likelihood ratio test statistic is the chi-square distribution. Some simulations and a real data analysis are conducted to illustrate the proposed method.