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.

翻译：差分隐私（DP）为在保护数据集中个体信息的前提下发布统计量提供了严格的理论框架。尽管差分隐私线性回归已取得显著进展，但现有方法几乎完全针对项目级DP场景，即每个用户仅贡献单次观测。然而众多科学与经济应用涉及纵向或面板数据，其中每个用户贡献多个相互依赖的观测值。在此类场景中，项目级DP无法提供充分保护，而用户级DP——保护个体完整轨迹——才是恰当的隐私定义。我们构建了用户级DP下纵向线性回归估计与推断的完整框架。提出基于局部回归聚合的用户级隐私回归估计量，并在短程依赖条件下建立有限样本保证与渐近正态性。针对推断问题，我们开发了私有化、偏差校正的协方差估计器，该估计器自动保持异方差与自相关性一致。这些成果首次为依赖条件下的纵向线性回归提供了实用的用户级DP估计与推断统一框架，兼具坚实的理论保证与优越的实证性能。