ABSTRACT
We saw in Chapter 9 that to construct estimates of low dimensional Euclidean parame-
ters in semiparametric models we need to estimate infinite dimensional parameters such as
curves. Examples are densities and derivatives of densities on the one hand and conditional
expectations on the other. These quantities, which will be considered in this chapter and
the next, are not defined for discrete distributions and, so, as we saw in Section I.5 we need
to consider regularized approximations to these parameters before we can construct empir-
ical plug-in estimates. This is not a consequence of our needing to estimate functions but
rather of the irregular nature of these parameters. For instance, we can estimate distribution
functions using plug-in estimates without regularizing.
