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

2025-08-10

AI Summary

Statistical inference for generalized linear models (GLMs) with high-dimensional longitudinal clustered data remains challenging, particularly under conventional sparsity assumptions. Method: This paper proposes a desparsified Dantzig selector approach that relaxes the strict sparsity requirement and achieves asymptotically optimal efficiency when the working correlation structure is correctly specified. By integrating Dantzig selector-based regularization with desparsification correction, the method unifies inference for both linear and generalized linear models. Contribution/Results: We establish consistency and asymptotic normality of the estimator under mild regularity conditions. Numerical experiments demonstrate superior finite-sample performance over existing methods for both continuous and binary outcomes. Applied to bacterial riboflavin production genetic data, the method significantly improves accuracy and interpretability in inferring key gene effects.

Technology Category

• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Graphical Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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.

Problem

• Inference for high-dimensional longitudinal generalized linear models
• De-sparsified Dantzig-selector for regression with theoretical guarantees
• Method evaluation via simulations and genetics dataset application

Innovation

• De-sparsified Dantzig-type estimator for regression
• Theoretical justification for linear models
• Application to genetics dataset analysis