I propose kernel ridge regression estimators for long term causal inference, where a short term experimental data set containing randomized treatment and short term surrogates is fused with a long term observational data set containing short term surrogates and long term outcomes. I propose estimators of treatment effects, dose responses, and counterfactual distributions with closed form solutions in terms of kernel matrix operations. I allow covariates, treatment, and surrogates to be discrete or continuous, and low, high, or infinite dimensional. For long term treatment effects, I prove $\sqrt{n}$ consistency, Gaussian approximation, and semiparametric efficiency. For long term dose responses, I prove uniform consistency with finite sample rates. For long term counterfactual distributions, I prove convergence in distribution.

翻译：我建议使用内核脊回归估计器进行长期因果推断,其中含有随机处理和短期代孕的短期实验数据集与含有短期代孕和长期结果的长期观察数据集结合。我建议使用内核矩阵操作中处理效果、剂量反应和具有封闭形式解决方案的反事实分布估计器。我允许共变、治疗和代孕是离散或连续的,低、高或无限的。对于长期治疗效果,我证明$\sqrt{n}$的一致性、高斯近似值和半对称效率。对于长期剂量反应,我证明与有限样本率的一致性。对于长期反事实分布,我证明分布一致。