  We consider the problem of estimating the value of a linear functional in
nonparametric instrumental regression, where in the presence of an instrument W
a response Y is modeled in dependence of an endogenous explanatory variable Z.
The proposed estimator is based on dimension reduction and additional
thresholding. The minimax optimal rate of convergence of the estimator is
derived assuming that the structural function and the representer of the linear
functional belong to some ellipsoids which are in a certain sense linked to the
conditional expectation operator of Z given W. We illustrate these results by
considering classical smoothness assumptions.
