  We consider the problem of estimating the value l({\phi}) of a linear
functional, where the structural function {\phi} models a nonparametric
relationship in presence of instrumental variables. We propose a plug-in
estimator which is based on a dimension reduction technique and additional
thresholding. It is shown that this estimator is consistent and can attain the
minimax optimal rate of convergence under additional regularity conditions.
This, however, requires an optimal choice of the dimension parameter m
depending on certain characteristics of the structural function {\phi} and the
joint distribution of the regressor and the instrument, which are unknown in
practice. We propose a fully data driven choice of m which combines model
selection and Lepski's method. We show that the adaptive estimator attains the
optimal rate of convergence up to a logarithmic factor. The theory in this
paper is illustrated by considering classical smoothness assumptions and we
discuss examples such as pointwise estimation or estimation of averages of the
structural function {\phi}.
