Generalized Kernel Ridge Regression for Long Term Causal Inference: Treatment Effects, Dose Responses, and Counterfactual Distributions

• URL: http://arxiv.org/abs/2201.05139v1
• Date: Thu, 13 Jan 2022 18:51:56 GMT
• Title: Generalized Kernel Ridge Regression for Long Term Causal Inference: Treatment Effects, Dose Responses, and Counterfactual Distributions
• Authors: Rahul Singh
• Abstract summary: I propose estimators of treatment effects, dose responses, and counterfactual distributions. For long term treatment effects, I prove $sqrtn$ consistency, Gaussian approximation, and semiparametric efficiency. For long term dose responses, I prove uniform consistency with finite sample rates.
• Score: 6.441975792340023
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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