让时间说明：中断时间序列的识别与高斯过程估计
Let Time Tell: Identification and Gaussian Process Estimation for Interrupted Time Series
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中文总结 AI 辅助
该研究针对中断时间序列设计中同期控制变量不可用的问题，提出基于高斯过程回归的反事实估计方法，通过偏差分解和不确定性量化保证估计合理性，并用R包gpss实现。
中文摘要 AI 辅助
我们研究中断时间序列设计中的因果推断，其中处理同时影响所有单元，因此双重差分法和合成控制法所用的同期控制变量不可用，反事实必须从单元自身的处理前历史中推断。我们在潜在结果框架内建立识别，并通过高斯过程回归估计反事实。该估计器不局限于单一最佳拟合趋势，而是保留与处理前序列一致的函数，并在推断放大这些函数分歧的区间加宽其范围。将其与再生核希尔伯特空间理论关联，我们推导了偏差分解，分离出推断放大的分量以及该分量的最坏情况界，证明高斯过程估计器的后验方差是感知推断的不确定性量化。该区间的闭式形式等于模型类在与处理前数据一致的函数中允许的最坏情况分歧。该方法通过校准模拟和对最高法院Heller判决后的手枪购买情况分析进行说明，该判决是一种普遍处理，其实际效果集中在单一司法管辖区。R包gpss实现了该方法。
英文摘要
We study causal inference in interrupted time series designs where a treatment affects every unit simultaneously, so that the contemporaneous controls used by difference-in-differences and synthetic control are unavailable and the counterfactual must be extrapolated from a unit's own pre-treatment history. We establish identification within the potential outcomes framework and estimate the counterfactual by Gaussian process regression. Rather than committing to a single best-fitting trend, the estimator retains the functions consistent with the pre-treatment series and widens its intervals where extrapolation magnifies their divergence. Connecting it to reproducing kernel Hilbert space theory, we derive a bias decomposition that isolates the component extrapolation inflates and a worst-case bound on that component, justifying the Gaussian process estimator's posterior variance as extrapolation-aware uncertainty quantification. In closed form, the band equals the worst-case divergence the model class permits among functions consistent with the pre-treatment data. The method is illustrated with calibrated simulations and an analysis of handgun purchases after the Supreme Court's Heller decision, a universal treatment whose practical effect concentrates in a single jurisdiction. An R package, gpss, implements the approach.
