  We study multiply robust (MR) estimators of the longitudinal g-computation
formula of Robins (1986). In the first part of this paper we review and extend
the recently proposed parametric multiply robust estimators of
Tchetgen-Tchetgen (2009) and Molina, Rotnitzky, Sued and Robins (2017). In the
second part of the paper we derive multiply and doubly robust estimators that
use non-parametric machine-learning (ML) estimators of nuisance functions in
lieu of parametric models. We use sample splitting to avoid the need for
Donsker conditions, thereby allowing an analyst to select the ML algorithms of
their choosing. We contrast the asymptotic behavior of our non-parametric
doubly robust and multiply robust estimators. In particular, we derive formulas
for their asymptotic bias. Examining these formulas we conclude that although,
under certain data generating laws, the rate at which the bias of the MR
estimator converges to zero can exceed that of the DR estimator, nonetheless,
under most laws, the bias of the DR and MR estimators converge to zero at the
same rate.
