Differentially Private Inference for Longitudinal Linear Regression

• URL: http://arxiv.org/abs/2601.10626v1
• Date: Thu, 15 Jan 2026 17:47:02 GMT
• Title: Differentially Private Inference for Longitudinal Linear Regression
• Authors: Getoar Sopa, Marco Avella Medina, Cynthia Rush,
• Abstract summary: We develop a comprehensive framework for estimation and inference in longitudinal linear regression under user-level DP.<n>For inference, we develop a privatized estimator that is automatically heteroskedasticity- and autocorrelation-consistent.<n>These results provide the first unified framework for practical user-level DP estimation and inference.
• Score: 9.16331221881594
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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