Locally sparse estimator of generalized varying coefficient model for asynchronous longitudinal data

In longitudinal study, it is common that response and covariate are not measured at the same time, which complicates the analysis to a large extent. In this paper, we take into account the estimation of generalized varying coefficient model with such asynchronous observations. A penalized kernel-weighted estimating equation is constructed through kernel technique in the framework of functional data analysis. Moreover, local sparsity is also considered in the estimating equation to improve the interpretability of the estimate. We extend the iteratively reweighted least squares (IRLS) algorithm in our computation. The theoretical properties are established in terms of both consistency and sparsistency, and the simulation studies further verify the satisfying performance of our method when compared with existing approaches. The method is applied to an AIDS study to reveal its practical merits.