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.

翻译：我们考虑的是具有随机效应的稀有高维差异系数模型,一种灵活的线性模型,允许共变和系数随时间产生功能依赖性。对于每个人,我们观察的是分散抽样反应和共变因时间和时间而变化。在固定和常见或随机的抽样时间中,我们建议一种预测程序,用于对所有不同系数进行实证估计。我们扩大这个估计数据,为固定数量的不同系数构建信任带。