  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.
