  When estimating the direct and indirect causal effects using the influence
function-based estimator of the mediation functional, it is crucial to
understand what aspects of the treatment, the mediator, and the outcome mean
mechanisms should be focused on. Specifically, considering them as nuisance
functions and attempting to fit these nuisance functions as accurate as
possible is not necessarily the best approach to take. In this work, we propose
a two-stage estimation strategy for the nuisance functions that estimates the
nuisance functions based on the role they play in the structure of the bias of
the influence function-based estimator of the mediation functional. We provide
robustness analysis of the proposed method, as well as sufficient conditions
for consistency and asymptotic normality of the estimator of the parameter of
interest.
