  There has been increasing interest in recent years in the development of
approaches to estimate causal effects when the number of potential confounders
is prohibitively large. This growth in interest has led to a number of
potential estimators one could use in this setting. Each of these estimators
has different operating characteristics, and it is unlikely that one estimator
will outperform all others across all possible scenarios. Coupling this with
the fact that an analyst can never know which approach is best for their
particular data, we propose a synthetic estimator that averages over a set of
candidate estimators. Averaging is widely used in statistics for problems such
as prediction, where there are many possible models, and averaging can improve
performance and increase robustness to using incorrect models. We show that
these ideas carry over into the estimation of causal effects in
high-dimensional scenarios. We show theoretically that averaging provides
robustness against choosing a bad model, and show empirically via simulation
that the averaging estimator performs quite well, and in most cases nearly as
well as the best among all possible candidate estimators. Finally, we
illustrate these ideas in an environmental wide association study and see that
averaging provides the largest benefit in the more difficult scenarios that
have large numbers of confounders.
