High-dimensional Longitudinal Inference via a De-sparsified Dantzig-Selector

TL;DR

This paper introduces a de-sparsified Dantzig-Selector for high-dimensional longitudinal data, enabling valid inference in complex models with applications to genetics.

Contribution

It develops a novel de-sparsified estimator for high-dimensional generalized linear models with longitudinal data, providing theoretical guarantees and practical effectiveness.

Findings

Estimator achieves asymptotic efficiency under correct correlation specification.

Method performs well for continuous and binary data in simulations.

Applied successfully to genetics data on bacterial riboflavin production.

Abstract

In this paper, we consider statistical inference with generalized linear models in high dimensions under a longitudinal clustered data framework. Specifically, we propose a de-sparsified version of an initial Dantzig-type regularized estimator in regression settings and provide theoretical justification for both linear and generalized linear models. We present extensive numerical simulations demonstrating the effectiveness of our method for continuous and binary data. For continuous outcomes under linear models, we show that our estimator asymptotically attains an appropriate efficiency bound when the correlation structure is correctly specified. We conclude with an application of our method to a well-established genetics dataset, with bacterial riboflavin production as the outcome of interest.