Abstract: In longitudinal studies, it is common that the response and the covariate are not measured at the same time, which complicates the subsequent analysis. In this study, we consider the estimation of a generalized varying coefficient model with such asynchronous observations. We construct a penalized kernel-weighted estimating equation using the kernel technique in a functional data analysis framework. Moreover, we consider local sparsity in the estimating equation to improve the interpretability of the estimate. We extend the iteratively reweighted least squares algorithm in our computation, and establish the theoretical properties of the proposed method, including the consistency, sparsistency, and asymptotic distribution. Lastly, we use simulation studies to verify the performance of our method, and demonstrate the method by applying it to data from a study on women’s health.

Keywords words and phrases: Asynchronous observation, functional data analysis, generalized varying coefficient model, kernel technique, local sparsity.