Time-dynamic Varying Coefficient Models for Longitudinal Data

Abstract

In this thesis, we propose a varying coefficient model that can be applied to longitudinal or functional data. The varying coefficient model captures the relationship between the response and the covariates with coefficient functions that are affected by smoothing variables. The varying coefficient model is a structured nonparametric model, and it can easily interpret the effects of the covariates. To avoid the curse of dimensionality, we propose the time-dynamic varying coefficient model as a structured nonparametric model. Also, we construct an iterative algorithm for estimation by extending the smooth backfitting method so that the estimator is defined as a projection of the full-dimensional estimator onto the additive function space with $L_2$-sense. We show that the proposed algorithm achieves uniform convergence with exponential rate and then study the asymptotic property of the estimator. Based on the numerical study of performances, we apply air quality data to the time-dynamic varying coefficient model for a real data analysis.