  In this article we study a class of parameters with the so-called `mixed bias
property'. For parameters with this property, the bias of the semiparametric
efficient one step estimator is equal to the mean of the product of the
estimation errors of two nuisance functions. In non-parametric models,
parameters with the mixed bias property admit so-called rate doubly robust
estimators, i.e. estimators that are consistent and asymptotically normal when
one succeeds in estimating both nuisance functions at sufficiently fast rates,
with the possibility of trading off slower rates of convergence for the
estimator of one of the nuisance functions with faster rates for the estimator
of the other nuisance. We show that the class of parameters with the mixed bias
property strictly includes two recently studied classes of parameters which, in
turn, include many parameters of interest in causal inference. We characterize
the form of parameters with the mixed bias property and of their influence
functions. Furthermore, we derive two functional moment equations, each being
solved at one of the two nuisance functions, as well as, two functional loss
functions, each being minimized at one of the two nuisance functions. These
loss functions can be used to derive loss based penalized estimators of the
nuisance functions.
