  Evaluating treatments received by one population for application to a
different target population of scientific interest is a central problem in
causal inference from observational studies. We study the minimax linear
estimator of the treatment-specific mean outcome on a target population and
provide a theoretical basis for inference based on it. In particular, we
provide a justification for the common practice of ignoring bias when building
confidence intervals with these linear estimators. Focusing on the case that
the class of the unknown outcome function is the unit ball of a reproducing
kernel Hilbert space, we show that the resulting linear estimator is
asymptotically optimal under conditions only marginally stronger than those
used with augmented estimators. We establish bounds attesting to the
estimator's good finite sample properties. In an extensive simulation study, we
observe promising performance of the estimator throughout a wide range of
sample sizes, noise levels, and levels of overlap between the covariate
distributions of the treated and target populations.
