  In the world of targeted learning, cross-validated targeted maximum
likelihood estimators, CV-TMLE [Zheng:2010aa], has a distinct advantage over
TMLE [Laan:2006aa] in that one less condition is required of CV-TMLE in order
to achieve asymptotic efficiency in the nonparametric or semiparametric
settings. CV-TMLE as originally formulated, consists of averaging usually 10
(for 10-fold cross-validation) parameter estimates, each of which is performed
on a validation set separate from where the initial fit was trained. The
targeting step is usually performed as a pooled regression over all validation
folds but in each fold, we separately evaluate any means as well as the
parameter estimate. One nice thing about CV-TMLE, is that we average 10 plug-in
estimates so the plug-in quality of preserving the natural parameter bounds is
respected. Our adjustment of this procedure also preserves the plug-in
characteristic as well as avoids the donsker condtion. The advantage of our
procedure is the implementation of the targeting is identical to that of a
regular TMLE, once all the validation set initial predictions have been formed.
In short, we stack the validation set predictions and pretend as if we have a
regular TMLE, which is not necessarily quite a plug-in estimator on each fold
but overall will perform asymptotically the same and might have some slight
advantage, a subject for future research. In the case of average treatment
effect, treatment specific mean and mean outcome under a stochastic
intervention, the procedure overlaps exactly with the originally formulated
CV-TMLE with a pooled regression for the targeting.
