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Differentially Private Inference for Longitudinal Linear Regression

Published: January 15, 2026 | arXiv ID: 2601.10626v1

By: Getoar Sopa, Marco Avella Medina, Cynthia Rush

Potential Business Impact:

Keeps private data safe in long-term studies.

Business Areas:
Predictive Analytics Artificial Intelligence, Data and Analytics, Software

Differential Privacy (DP) provides a rigorous framework for releasing statistics while protecting individual information present in a dataset. Although substantial progress has been made on differentially private linear regression, existing methods almost exclusively address the item-level DP setting, where each user contributes a single observation. Many scientific and economic applications instead involve longitudinal or panel data, in which each user contributes multiple dependent observations. In these settings, item-level DP offers inadequate protection, and user-level DP - shielding an individual's entire trajectory - is the appropriate privacy notion. We develop a comprehensive framework for estimation and inference in longitudinal linear regression under user-level DP. We propose a user-level private regression estimator based on aggregating local regressions, and we establish finite-sample guarantees and asymptotic normality under short-range dependence. For inference, we develop a privatized, bias-corrected covariance estimator that is automatically heteroskedasticity- and autocorrelation-consistent. These results provide the first unified framework for practical user-level DP estimation and inference in longitudinal linear regression under dependence, with strong theoretical guarantees and promising empirical performance.

Page Count
68 pages

Category
Mathematics:
Statistics Theory