  Targeted maximum likelihood estimation (TMLE) is a general method for
estimating parameters in semiparametric and nonparametric models. Each
iteration of TMLE involves fitting a parametric submodel that targets the
parameter of interest. We investigate the use of exponential families to define
the parametric submodel. This implementation of TMLE gives a general approach
for estimating any smooth parameter in the nonparametric model. A computational
advantage of this approach is that each iteration of TMLE involves estimation
of a parameter in an exponential family, which is a convex optimization problem
for which software implementing reliable and computationally efficient methods
exists. We illustrate the method in three estimation problems, involving the
mean of an outcome missing at random, the parameter of a median regression
model, and the causal effect of a continuous exposure, respectively. We conduct
a simulation study comparing different choices for the parametric submodel,
focusing on the first of these problems. To the best of our knowledge, this is
the first study investigating robustness of TMLE to different specifications of
the parametric submodel. We find that the choice of submodel can have an
important impact on the behavior of the estimator in finite samples.
