Network Functional Varying Coefficient Model

We consider functional responses with network dependence observed for each individual at irregular time points. To model both the interindividual and within-individual dynamic correlation, we propose a varying coefficient (NFVC) model. The response of is characterized by linear combination from its connected nodes exogenous covariates. All coefficients are allowed to be dependent. NFVC adds richness classical autoregression regression models. overcome complexity caused interdependence, devise special nonparametric least-squares-type estimator, which feasible when points different individuals. estimator takes advantage sparsity structure reduce computational burden. further conduct principal component analysis, novel covariance function estimation method proposed studied. Theoretical properties our estimators, involve techniques related empirical processes, nonparametrics, data analysis various concentration inequalities, analyzed. analyze social dataset illustrate powerfulness procedure.