High-Dimensional Varying Coefficient Models with Functional Random Effects

Abstract: We consider a sparse high-dimensional varying coefficients model with random effects, a flexible linear model allowing covariates and coefficients to have a functional dependence with time. For each individual, we observe discretely sampled responses and covariates as a function of time as well as time invariant covariates. Under sampling times that are either fixed and common or random and independent amongst individuals, we propose a projection procedure for the empirical estimation of all varying coefficients. We extend this estimator to construct confidence bands for a fixed number of varying coefficients.