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

This paper focuses on decorrelated empirical likelihood-based inference for longitudinal data with ultrahigh-dimensional covariates. The primary issues we aim to address involve parameter estimation and hypothesis testing for a low-dimensional parameter of interest. Under the framework of the generalized linear model, we initially consider the within-subject correlation by linearizing the precision matrix with certain known matrices, which retains optimality even if the working correlated structure is misspecified. Coupled with the decorrelated matrix, we then eliminate the influence of nuisance parameters on the estimation procedure. The proposed approach not only yields more efficient estimators compared to generalized decorrelated estimating equations but also shares the same asymptotic variance as quadratic decorrelated inference function based methods. Furthermore, we define the decorrelated empirical log-likelihood ratio test statistic to assess the significance of regression coefficients. Finally, to evaluate the performance of the proposed procedure, we conduct simulation studies and apply it to a real data example.