  Consider a quite arbitrary (semi)parametric model with a Euclidean parameter
of interest and assume that an asymptotically (semi)parametrically efficient
estimator of it is given. If the parameter of interest is known to lie on a
general surface (image of a continuously differentiable vector valued
function), we have a submodel in which this constrained Euclidean parameter may
be rewritten in terms of a lower-dimensional Euclidean parameter of interest.
An estimator of this underlying parameter is constructed based on the original
estimator, and it is shown to be (semi)parametrically efficient. It is proved
that the efficient score function for the underlying parameter is determined by
the efficient score function for the original parameter and the Jacobian of the
function defining the general surface, via a chain rule for score functions.
Efficient estimation of the constrained Euclidean parameter itself is
considered as well.
  Our general estimation method is applied to location-scale, Gaussian copula
and semiparametric regression models, and to parametric models under linear
restrictions.
