Time-dynamic varying coefficient models for longitudinal data

A new varying coefficient model that relates functional response to functional predictors is proposed and studied. The model accommodates the influence of the functional predictors on the time-varying coefficient functions. A powerful kernel smoothing technique is developed for estimating the model with longitudinal observations of the functional response and predictors. The method involves a backfitting iteration that is based on alternating conditional expectation. The convergence of the algorithm is established and the asymptotic distribution of the coefficient function estimators is derived. It is shown that the method works well for finite sample sizes via simulation studies. The proposed model and method are also applied to analyzing an air quality dataset.