Estimation for High-Dimensional Linear Mixed-Effects Models Using $\ell_1$-Penalization

TL;DR

This paper introduces an $ ext{L}_1$-penalized estimation method for high-dimensional linear mixed-effects models, providing theoretical guarantees and demonstrating effectiveness on simulated and real data.

Contribution

It presents a novel $ ext{L}_1$-penalized approach for high-dimensional mixed-effects models with proven consistency and an efficient algorithm.

Findings

Method achieves consistency and oracle optimality.

Algorithm converges reliably in practice.

Effective on both simulated and real datasets.

Abstract

We propose an $\ell_1$-penalized estimation procedure for high-dimensional linear mixed-effects models. The models are useful whenever there is a grouping structure among high-dimensional observations, i.e. for clustered data. We prove a consistency and an oracle optimality result and we develop an algorithm with provable numerical convergence. Furthermore, we demonstrate the performance of the method on simulated and a real high-dimensional data set.