High-Dimensional Varying Coefficient Models with Functional Random Effects

TL;DR

This paper introduces a flexible high-dimensional varying coefficient model with functional random effects, providing a projection-based estimation method and confidence bands for time-dependent covariate effects.

Contribution

It develops a novel projection procedure for empirical estimation and confidence band construction in high-dimensional models with functional random effects.

Findings

Effective estimation of varying coefficients from discretely sampled data

Construction of confidence bands for selected coefficients

Applicable under fixed or random sampling times

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.