Asymptotic behaviour of estimation equations with functional nuisance or working parameter

We are concerned with the asymptotic theory of semiparametric
estimation equations. We are dealing with estimation equations
which have a parametric component of interest and a functional
(nonparametric) nuisance component. We give sufficient conditions
for the existence and the asymptotic normality of a consistent
estimation equation estimator for the parameter of interest. These
conditions concern the asymptotic distribution of the estimation
function and of its derivative as well as the effect of the
functional nuisance part in the estimation equation. In order to
treat the nonparametric component we introduce a general
differential calculus and a general mean value theorem. For the
nonparametric part in the estimation equation we distinguish two
cases: the situation of a (classical) nuisance parameter and the
case of a so called working parameter. As a special case we get
regularity conditions for estimation equations with finite
dimensional nuisance or working parameter. As an example we present
the semiparametric linear regression model.