<p>The main objective of this paper is to derive the efficiency bounds for estimating certain linear functionals of an unknown structural function when the latter is not itself a conditional expectation.

We introduce a notion of median uncorrelation that is a natural extension of mean (linear) uncorrelation. A scalar random variable Y is median uncorrelated with a k-dimensional random vector X if and only if the slope from an LAD regression of Y on X is zero. Using this simple definition, we...