This letter considers the problem of estimating expected values of functions that are inversely weighted by an unknown density using the k-Nearest Neighbor method. L²-consistency is established. The proposed estimator is also shown to be asymptotically semiparametric efficient. Some limited...

This letter considers the problem of estimating expected values of functions that are inversely weighted by an unknown density using the k-Nearest Neighbor method. L²-consistency is established. The proposed estimator is also shown to be asymptotically semiparametric efficient. Some limited...

We prove the strong consistency, uniformly in the bandwidth, of the smooth varying coefficient conditional least squares estimator. Our results justify data-driven choices of bandwidths, such as Silverman's rule-of thumb, or standard cross-validation, that are usually implemented by most...