Estimation and model identification of longitudinal data time-varying nonparametric models

In this paper, we consider nonparametric regression modeling for longitudinal data. An important modeling choice is that the covariate effect may change dynamically with time by using a bivariate link function. Comparing with Jiang and Wang (2010, 2011), and Zhang et al. (2013) we make two distinct contributions to this important class of models. First, we show theoretically and empirically that taking the within-subject correlation into account can improve the estimation efficiency for the bivariate link function. Second, we propose a novel method involving a shrinkage estimation technique to identify consistently whether the effect of covariates is time-varying. Simulation studies are conducted to assess the finite-sample performance and a real data example is analyzed to illustrate the proposed methods.