Generalized Kernel Ridge Regression for Causal Inference with Missing-at-Random Sample Selection
This work addresses causal inference challenges for researchers dealing with missing data in observational studies, offering a nonparametric and semiparametric framework with theoretical guarantees.
The paper tackles the problem of estimating causal effects when outcomes are missing-at-random in selected samples, proposing kernel ridge regression estimators for dose response curves and treatment effects. It proves uniform consistency with finite sample rates for continuous treatments and root-n consistency with semiparametric efficiency for discrete treatments.
I propose kernel ridge regression estimators for nonparametric dose response curves and semiparametric treatment effects in the setting where an analyst has access to a selected sample rather than a random sample; only for select observations, the outcome is observed. I assume selection is as good as random conditional on treatment and a sufficiently rich set of observed covariates, where the covariates are allowed to cause treatment or be caused by treatment -- an extension of missingness-at-random (MAR). I propose estimators of means, increments, and distributions of counterfactual outcomes with closed form solutions in terms of kernel matrix operations, allowing treatment and covariates to be discrete or continuous, and low, high, or infinite dimensional. For the continuous treatment case, I prove uniform consistency with finite sample rates. For the discrete treatment case, I prove root-n consistency, Gaussian approximation, and semiparametric efficiency.