  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.
