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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